Journal articles: 'Auxiliary modulating dynamical systems'

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Liu, Jie, Da-Yan Liu, Driss Boutat, Xuefeng Zhang, and Ze-Hao Wu. "Innovative non-asymptotic and robust estimation method using auxiliary modulating dynamical systems." Automatica 152 (June 2023): 110953. http://dx.doi.org/10.1016/j.automatica.2023.110953.

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Stark, Oliver, Marius Eckert, Albertus Johannes Malan, and Sören Hohmann. "Fractional Systems’ Identification Based on Implicit Modulating Functions." Mathematics 10, no. 21 (November 3, 2022): 4106. http://dx.doi.org/10.3390/math10214106.

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This paper presents a new method for parameter identification based on the modulating function method for commensurable fractional-order models. The novelty of the method lies in the automatic determination of a specific modulating function by controlling a model-based auxiliary system, instead of applying and parameterizing a generic modulating function. The input signal of the model-based auxiliary system used to determine the modulating function is designed such that a separate identification of each individual parameter of the fractional-order model is enabled. This eliminates the shortcomings of the common modulating function method in which a modulating function must be adapted to the investigated system heuristically.

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Catanach, Thomas A., and James L. Beck. "Bayesian System Identification using auxiliary stochastic dynamical systems." International Journal of Non-Linear Mechanics 94 (September 2017): 72–83. http://dx.doi.org/10.1016/j.ijnonlinmec.2017.03.012.

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Grechko, D. A., N. V. Barabash, and V. N. Belykh. "Homoclinic Orbits and Chaos in Nonlinear Dynamical Systems: Auxiliary Systems Method." Lobachevskii Journal of Mathematics 42, no. 14 (December 2021): 3365–71. http://dx.doi.org/10.1134/s199508022202007x.

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Fang-Hong, Xiao, Yan Gui-Rong, and Zhang Xin-Wu. "Effect of signal modulating noise in bistable stochastic dynamical systems." Chinese Physics 12, no. 9 (August 29, 2003): 946–50. http://dx.doi.org/10.1088/1009-1963/12/9/304.

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El Allaoui, Abdelati, Said Melliani, and Lalla Saadia Chadli. "Stability of Fuzzy Dynamical Systems via Lyapunov Functions." International Journal of Differential Equations 2020 (August 1, 2020): 1–7. http://dx.doi.org/10.1155/2020/6218424.

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The purpose of this paper is to introduce the concept of fuzzy Lyapunov functions to study the notion of stability of equilibrium points for fuzzy dynamical systems associated with fuzzy initial value problems, through the principle of Zadeh. Our contribution consists in a qualitative characterization of stability by a study of the trajectories of fuzzy dynamical systems, using auxiliary functions, and they will be called fuzzy Lyapunov functions. And, among the main results that have been proven is that the existence of fuzzy Lyapunov functions is a necessary and sufficient condition for stability. Some examples are given to illustrate the obtained results.

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ZHANG, YONGXIANG. "CHARACTERIZING FRACTAL BASIN BOUNDARIES FOR PLANAR SWITCHED SYSTEMS." Fractals 25, no. 03 (May 18, 2017): 1750031. http://dx.doi.org/10.1142/s0218348x17500311.

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This paper is to introduce some analytical tools to characterize the properties of fractal basin boundaries for planar switched systems (with time-dependent switching). The characterizing methods are based on the view point of limit sets and prime ends. By constructing the auxiliary dynamical system, the fractal basin boundaries of planar switched systems can be proved if every diverging path in the basin of associated auxiliary system has the entire basin boundary as its limit set. Fractal property is also verified if every prime end that is defined in the basin of associated auxiliary system is a prime end of type 3 and all other prime ends are of type 1. Bifurcations of fractal basin boundary are investigated by analyzing what types of prime ends in the basin are involved. The fractal basin boundary of switched system is also described by the indecomposable continuum.

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Tang, Jia-Liang, Gabriel Alvarado Barrios, Enrique Solano, and Francisco Albarrán-Arriagada. "Tunable Non-Markovianity for Bosonic Quantum Memristors." Entropy 25, no. 5 (May 6, 2023): 756. http://dx.doi.org/10.3390/e25050756.

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We studied the tunable control of the non-Markovianity of a bosonic mode due to its coupling to a set of auxiliary qubits, both embedded in a thermal reservoir. Specifically, we considered a single cavity mode coupled to auxiliary qubits described by the Tavis–Cummings model. As a figure of merit, we define the dynamical non-Markovianity as the tendency of a system to return to its initial state, instead of evolving monotonically to its steady state. We studied how this dynamical non-Markovianity can be manipulated in terms of the qubit frequency. We found that the control of the auxiliary systems affects the cavity dynamics as an effective time-dependent decay rate. Finally, we show how this tunable time-dependent decay rate can be tuned to engineer bosonic quantum memristors, involving memory effects that are fundamental for developing neuromorphic quantum technologies.

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Sabi’u, Jamilu, Mustafa Inc, Temesgen Leta, Dumitru Baleanu, and Hadi Rezazadeh. "Dynamical behaviour of the Joseph-Egri equation." Thermal Science 27, Spec. issue 1 (2023): 19–28. http://dx.doi.org/10.2298/tsci23s1019s.

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We investigate traveling wave solutions to the Joseph-Egri equation via extended auxiliary equation technique. We have determined stationary points of the dynamical systems by using bifurcation method. We also acquire cusp, periodic and homoclinic orbits. The investigated solutions are entirely different from the reported in the liter?ature. However, some of the reported solutions are plotted to understand the physical application of the considered model using renowned mathematical software.

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Pumaricra Rojas, David, Matti Noack, Johann Reger, and Gustavo Pérez-Zúñiga. "State Estimation for Coupled Reaction-Diffusion PDE Systems Using Modulating Functions." Sensors 22, no. 13 (July 2, 2022): 5008. http://dx.doi.org/10.3390/s22135008.

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Many systems with distributed dynamics are described by partial differential equations (PDEs). Coupled reaction-diffusion equations are a particular type of these systems. The measurement of the state over the entire spatial domain is usually required for their control. However, it is often impossible to obtain full state information with physical sensors only. For this problem, observers are developed to estimate the state based on boundary measurements. The method presented applies the so-called modulating function method, relying on an orthonormal function basis representation. Auxiliary systems are generated from the original system by applying modulating functions and formulating annihilation conditions. It is extended by a decoupling matrix step. The calculated kernels are utilized for modulating the input and output signals over a receding time window to obtain the coefficients for the basis expansion for the desired state estimation. The developed algorithm and its real-time functionality are verified via simulation of an example system related to the dynamics of chemical tubular reactors and compared to the conventional backstepping observer. The method achieves a successful state reconstruction of the system while mitigating white noise induced by the sensor. Ultimately, the modulating function approach represents a solution for the distributed state estimation problem without solving a PDE online.

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Abe, Sumiyoshi. "Weak invariants in dissipative systems: action principle and Noether charge for kinetic theory." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 378, no. 2170 (March 30, 2020): 20190196. http://dx.doi.org/10.1098/rsta.2019.0196.

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In non-equilibrium classical thermostatistics, the state of a system may be described by not only dynamical/thermodynamical variables but also a kinetic distribution function. This ‘double structure’ bears some analogy with that in quantum thermodynamics, where both dynamical variables and the Hilbert space are involved. Recently, the concept of weak invariants has repeatedly been discussed in the context of quantum thermodynamics. A weak invariant is defined in such a way that its value changes in time but its expectation value is conserved under time evolution prescribed by a kinetic equation. Here, a new aspect of a weak invariant is revealed for the classical Fokker–Planck equation as an example of classical kinetic equations. The auxiliary field formalism is applied to the construction of the action for the kinetic equation. Then, it is shown that the auxiliary field is a weak invariant and is the Noether charge. The action is invariant under the transformation generated by the weak invariant. The result may shed light on possible roles of the symmetry principle in the kinetic descriptions of non-equilibrium systems. This article is part of the theme issue ‘Fundamental aspects of nonequilibrium thermodynamics’.

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MICHALSKI, Jacek. "Comparison of Auxiliary and Likelihood Particle Filters for State Estimation of Dynamical Systems." PRZEGLĄD ELEKTROTECHNICZNY 1, no. 12 (December 5, 2018): 88–92. http://dx.doi.org/10.15199/48.2018.12.19.

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Belinskiy, Boris P., and Peter Caithamer. "Stability of Dynamical Systems with a Multiplicative White Noise." Stochastics and Dynamics 03, no. 02 (June 2003): 187–212. http://dx.doi.org/10.1142/s021949370300070x.

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We discuss the behavior, for large values of time, of a class of linear mechanical systems with a white noise in their parameters. The initial conditions may be random as well but are independent of white noise. It is well known that a deterministic linear mechanical system with viscous damping is stable, i.e. its energy approaches zero as time increases. We calculate the expected energy and check that this behavior takes place in the case when the initial conditions are random but the parameters are not. When the parameters contain a random noise the expected energy may be infinite, approach zero, remain bounded, or increase with no bound. This regime is similar to but more interesting than the known regime for the solutions of differential equations with time-dependent periodic coefficients that describe the behavior of a mechanical system whose characteristics are periodic functions of time. We give necessary and sufficient conditions for stability of the systems considered in terms of the roots of an auxiliary equation. We explain why our approach may not be applied to some other models.

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Zheng, Hongpeng, Yulong Lei, and Pengxiang Song. "Designing the main controller of auxiliary braking systems for heavy-duty vehicles in nonemergency braking conditions." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 232, no. 9 (May 7, 2017): 1605–15. http://dx.doi.org/10.1177/0954406217706386.

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With the development of the road industry, heavy-duty vehicles now require additional braking power to fulfill their braking requirements. Auxiliary braking systems, which include a hydraulic retarder and an engine brake, can provide additional braking force in nonemergency braking conditions. A water medium retarder is a new type of hydraulic retarder that can convert the kinetic energy of a vehicle into the thermal energy of coolant. This study introduces a novel auxiliary braking system involving a water medium retarder and an engine brake for heavy-duty vehicles. The specific forces of heavy-duty vehicles and the auxiliary braking system are established. The control logic of the novel auxiliary braking system is assigned, and a main controller is designed to dynamically manage the entire braking process. The main controller includes controllers A and B, which handles the engine brake and water medium retarder, respectively. The heavy-duty vehicles dynamic system model is created using MATLAB/Simulink. Upon performance testing, simulation results show that the designed main controller can effectively and rapidly manage the auxiliary braking system, thus satisfying the braking requirements in any nonemergency braking condition. Even when the slope of a road changes, the main controller can extract dynamical forces as well as acceleration parameters and fulfill the braking requirements of vehicles.

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GOMOYUNOV, MIKHAIL, DMITRI KORNEV, and NIKOLAI LUKOYANOV. "GAME THEORY APPLICATIONS TO GUARANTEE OPTIMIZATION IN DYNAMICAL SYSTEMS WITH CONTROL DELAYS." International Game Theory Review 16, no. 02 (April 3, 2014): 1440010. http://dx.doi.org/10.1142/s0219198914400106.

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In this paper, a linear dynamical system controlled under the conditions of disturbances and with control delays is considered. The Euclidean norm of a set of the system motion deviations at given instants of time from given targets is minimized. Within the game-theoretical approach the problem of calculating the value of the optimal guaranteed result and constructing a positional (closed-loop) control law that ensures this result is posed. For this problem, a solution procedure based on the recurrent construction of upper convex hulls of auxiliary program functions is elaborated. Results of numerical simulations are given.

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WU, ZHAOYAN, XINCHU FU, and GUANRONG CHEN. "MONITORING THE TOPOLOGY OF GROWING DYNAMICAL NETWORKS." International Journal of Modern Physics C 21, no. 08 (August 2010): 1051–63. http://dx.doi.org/10.1142/s012918311001566x.

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In this paper, topology monitoring of growing networks is studied. When some new nodes are added into a network, the topology of the network is changed, which needs to be monitored in many applications. Some auxiliary systems (network monitors) are designed to achieve this goal. Both linear feedback control and adaptive strategy are applied to designing such network monitors. Based on the Lyapunov function method via constructing a potential or energy function decreasing along any solution of the system, and the LaSalle's invariance principle, which is a generalization of the Lyapunov function method, some sufficient conditions for achieving topology monitoring are obtained. Illustrative examples are provided to demonstrate the effectiveness of the new method.

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YAN, FANG, CUNCAI HUA, HAIHONG LIU, and ZENGRONG LIU. "THE EXACT TRAVELING WAVE SOLUTIONS AND THEIR BIFURCATIONS IN THE GARDNER AND GARDNER–KP EQUATIONS." International Journal of Bifurcation and Chaos 22, no. 05 (May 2012): 1250126. http://dx.doi.org/10.1142/s021812741250126x.

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By using the method of dynamical systems, this paper studies the exact traveling wave solutions and their bifurcations in the Gardner equation. Exact parametric representations of all wave solutions as well as the explicit analytic solutions are given. Moreover, several series of exact traveling wave solutions of the Gardner–KP equation are obtained via an auxiliary function method.

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Москаленко, О. И., Е. В. Евстифеев, and А. А. Короновский. "Метод определения характеристик перемежающейся обобщенной синхронизации на основе расчета локальных показателей Ляпунова." Письма в журнал технической физики 46, no. 16 (2020): 12. http://dx.doi.org/10.21883/pjtf.2020.16.49846.18359.

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Method for the laminar and turbulent phase detection in coupled dynamical systems being near the boundary of the generalized synchronization regime based on the calculation of local Lyapunov exponents has been proposed. The efficiency of the method has been testified using the systems with unidirectional coupling allowing the analysis of intermittency by the auxiliary system approach. The results of both methods have been compared with each other, a good agreement between them has been obtained.

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Azhmyakov, Vadim, and Ruben Velazquez. "On a Variational Approach to Optimization of Hybrid Mechanical Systems." Mathematical Problems in Engineering 2010 (2010): 1–13. http://dx.doi.org/10.1155/2010/978736.

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This paper deals with multiobjective optimization techniques for a class of hybrid optimal control problems in mechanical systems. We deal with general nonlinear hybrid control systems described by boundary-value problems associated with hybrid-type Euler-Lagrange or Hamilton equations. The variational structure of the corresponding solutions makes it possible to reduce the original “mechanical” problem to an auxiliary multiobjective programming reformulation. This approach motivates possible applications of theoretical and computational results from multiobjective optimization related to the original dynamical optimization problem. We consider first order optimality conditions for optimal control problems governed by hybrid mechanical systems and also discuss some conceptual algorithms.

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Tokmak, Fen, Mehmet Fen, and Marat Akhmet. "A novel criterion for unpredictable motions." Filomat 37, no. 18 (2023): 6151–60. http://dx.doi.org/10.2298/fil2318151t.

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We demonstrate the extension of unpredictable motions in coupled autonomous systems with skew product structure in the case that generalized synchronization takes place. Sufficient conditions for the existence of unpredictable motions in the dynamics of the response system are provided. The theoretical results are exemplified for coupled autonomous systems in which the drive is a hybrid dynamical system and the response is a Lorenz system. The auxiliary system approach and conditional Lyapunov exponents are utilized to detect the presence of generalized synchronization.

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Dykman, M. I., V. N. Smelyanskiy, D. G. Luchinsky, R. Mannella, P. V. E. McClintock, and N. D. Stein. "Large Fluctuations in a Periodically Driven Dynamical System." International Journal of Bifurcation and Chaos 08, no. 04 (April 1998): 747–54. http://dx.doi.org/10.1142/s0218127498000541.

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Fluctuations in a periodically driven overdamped oscillator are studied theoretically and experimentally in the limit of low noise intensity by investigation of their prehistory. It is shown that, for small noise intensity, fluctuations to points in coordinate space that are remote from the stable states occur along paths that form narrow tubes. The tubes are centered on the optimal paths corresponding to trajectories of an auxiliary Hamiltonian system. The optimal paths themselves, and the tubes of paths around them, are visualized through measurements of the prehistory probability distribution for an electronic model. Some general features of fluctuations in nonequilibrium systems, such as singularities in the pattern of optimal paths, the corresponding nondifferentiability of the generalized nonequilibrium potential, and the feasibility of their experimental investigation, are discussed.

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MANAVELLA, EDMUNDO C. "FADDEEV–JACKIW FORMALISM FOR CONSTRAINED SYSTEMS WITH GRASSMANN DYNAMICAL FIELD VARIABLES." International Journal of Modern Physics A 27, no. 24 (September 28, 2012): 1250145. http://dx.doi.org/10.1142/s0217751x1250145x.

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The Faddeev–Jackiw canonical quantization formalism for constrained systems with Grassmann dynamical variables within the framework of the field theory is reviewed. First, by means of a iterative process, the symplectic supermatrix is constructed and their associated constraints are found. Next, by taking into account the phase space of the system, the constraint structure is considered. It is found that, if there are no auxiliary dynamical field variables, the supermatrix whose elements are the Bose–Fermi brackets between the constraints associated with the independent dynamical field variables coincides with the symplectic supermatrix corresponding to these independent variables. An alternative procedure to obtain the first-class constraints is given. It is shown that for systems with gauge symmetries, by means of suitable gauge-fixing conditions, a nonsingular final symplectic supermatrix can be found. Then, two possible ways of calculating the Faddeev–Jackiw brackets are pointed out. The relation between the Faddeev–Jackiw and Dirac brackets is discussed. Throughout the previous developments, the Faddeev–Jackiw and Dirac algorithms are compared. Finally, the Faddeev–Jackiw canonical quantization method is applied to a simple model and the obtained results are compared with the ones corresponding to the use of the Dirac procedure on this model.

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AlShejari, A. A., M. A. Noor, and K. I. Noor. "Recent Developments in General Quasi Variational Inequalities." International Journal of Analysis and Applications 22 (May 20, 2024): 84. http://dx.doi.org/10.28924/2291-8639-22-2024-84.

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In this paper, we present a number of new and known numerical techniques for solving general quasi variational inequalities, introduced by Noor [34] in 1988, using various techniques including projection, Wiener-Hopf equations, auxiliary principle, dynamical systems coupled with finite difference approach and sensitivity analysis. Convergence analysis of these methods is investigated under suitable conditions. Sensitivity analysis is also investigated. Some special cases are discussed as applications of the main results. Several open problems are suggested for future research.

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Cassal-Quiroga, B. B., and E. Campos-Cantón. "Generation of Dynamical S-Boxes for Block Ciphers via Extended Logistic Map." Mathematical Problems in Engineering 2020 (March 19, 2020): 1–12. http://dx.doi.org/10.1155/2020/2702653.

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In this work, we present a simple algorithm to design n × n-bits substitution boxes (S-boxes) based on chaotic time series of the logistic map for different carrying capacities. The use of different carrying capacities in the chaotic map leads to low computational complexity, which is desirable to get high-speed communication systems. We generate a main sequence by means of two auxiliary sequences with uniform distribution via the logistic map for different carrying capacities. The elements of the main sequence are useful for generating the elements of an S-box. The auxiliary sequences are generated by considering lag time chaotic series; this helps to hide the chaotic map used. The U-shape distribution of logistic chaotic map is also avoided, in contrast with common chaos-based schemes without considering lag time chaotic series, and uncorrelated S-box elements are obtained. The proposed algorithm guarantees the generation of strong S-boxes that fulfill the following criteria: bijection, nonlinearity, strict avalanche criterion, output bits independence criterion, criterion of equiprobable input/output XOR distribution, and maximum expected linear probability. Finally, an application premised on polyalphabetic ciphers principle is developed to obtain a uniform distribution of the plaintext via dynamical S-boxes.

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Ebrahimi, Reza, Mostafa Ghayour, and Heshmatallah Mohammad Khanlo. "Effects of some design parameters on bifurcation behavior of a magnetically supported coaxial rotor in auxiliary bearings." Engineering Computations 34, no. 7 (October 2, 2017): 2379–95. http://dx.doi.org/10.1108/ec-04-2017-0141.

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Purpose This paper aims to present bifurcation analysis of a magnetically supported coaxial rotor model in auxiliary bearings, which includes gyroscopic moments of disks and geometric coupling of the magnetic actuators. Design/methodology/approach Ten nonlinear equations of motion were solved using the Runge–Kutta method. The vibration responses were analyzed using dynamic trajectories, power spectra, Poincaré maps, bifurcation diagrams and the maximum Lyapunov exponent. The analysis was carried out for different system parameters, namely, the inner shaft stiffness, inter-rotor bearing stiffness, auxiliary bearing stiffness and disk position. Findings It was shown that dynamics of the system could be significantly affected by varying these parameters, so that the system responses displayed a rich variety of nonlinear dynamical phenomena, including quasi-periodicity, chaos and jump. Next, some threshold values were provided with regard to the design of appropriate parameters for this system. Therefore, the proposed work can provide an effective means of gaining insights into the nonlinear dynamics of coaxial rotor–active magnetic bearing systems with auxiliary bearings in the future. Originality/value This paper considered the influences of the inner shaft stiffness, inter-rotor bearing stiffness, auxiliary bearing stiffness and disk position on the bifurcation behavior of a magnetically supported coaxial rotor system in auxiliary bearings.

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Pianta, Camilla, Roberto Capuzzo-Dolcetta, and Giovanni Carraro. "The Impact of Binaries on the Dynamical Mass Estimate of Dwarf Galaxies." Astrophysical Journal 939, no. 1 (October 26, 2022): 3. http://dx.doi.org/10.3847/1538-4357/ac9303.

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Abstract Binary stars are recognized to be important in driving the dynamical evolution of stellar systems and also in determining some of their observational features. In this study, we explore the role that binary stars have in modulating the estimates of the velocity dispersion of stellar systems. To this aim, we developed a tool that allows investigation of the dependence of synthetic velocity dispersion on a number of crucial quantities characterizing the binary content: binary fraction and the distributions of their mass ratio, eccentricity, and semimajor axis. As an application, we evaluate the impact that binary stars have on the estimation of the dynamical mass of dwarf spheroidal and ultrafaint dwarf galaxies, finding that it can be particularly relevant, especially for low-mass and low-density systems. These results bear profound implications for the interpretation of the measured velocity dispersion in such systems, since it weakens or relieves the claim for the need of large amounts of dark matter.

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Kretchmer, Joshua S., and Thomas F. Miller III. "Kinetically-constrained ring-polymer molecular dynamics for non-adiabatic chemistries involving solvent and donor–acceptor dynamical effects." Faraday Discussions 195 (2016): 191–214. http://dx.doi.org/10.1039/c6fd00143b.

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We investigate the performance of the recently developed kinetically-constrained ring polymer molecular dynamics (KC-RPMD) method for the description of model condensed-phase electron transfer (ET) reactions in which solvent and donor–acceptor dynamics play an important role. Comparison of KC-RPMD with results from Golden-Rule rate theories and numerically exact quantum dynamics calculations demonstrates that KC-RPMD accurately captures the combination of electronic- and nuclear-dynamical effects throughout the Marcus (intermediate solvent friction) and Zusman (large solvent friction) regimes of ET. It is also demonstrated that KC-RPMD accurately describes systems in which the magnitude of the diabatic coupling depends on the position of a dynamical donor–acceptor mode. In addition to these successes, however, we present an unsurprising failure of KC-RPMD to capture the enhancement of the ET rate in the low solvent friction regime associated with nuclear coherence effects. In this analysis, we re-visit several aspects of the original KC-RPMD formulation, including the form of the kinetic constraint and the choice of the mass of the auxiliary electronic variable. In particular, we introduce a Langevin bath for the auxiliary electronic variable to correct for its unphysically low coupling with the nuclear degrees of freedom. This work demonstrates that the KC-RPMD method is well suited for the direct simulation of non-adiabatic donor–acceptor chemistries associated with many complex systems, including those for which solvent dynamics plays an important role in the reaction mechanism.

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Aslan, İsmail. "Traveling Waves of DDEs with Rational Nonlinearity." International Journal of Nonlinear Sciences and Numerical Simulation 17, no. 5 (August 1, 2016): 243–48. http://dx.doi.org/10.1515/ijnsns-2016-0028.

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AbstractIt has been found that the dynamical behavior of many complex physical systems can be properly described by nonlinear DDEs. However, in the related literature, research focusing on such equations with rational nonlinearity is rare. Hence, the present study makes an attempt to fill the existing gap. To this end, we consider two distinct DDEs with rational nonlinearity. We observed that the model equations assume three kinds of traveling wave solutions; hyperbolic, trigonometric and rational including kink-type solitary waves and singular periodic solutions. Our discussion is based on the auxiliary equation method.

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Liu, Lizhi, Zilin Gao, and Yi Peng. "Synchronization Mechanism for Controlled Complex Networks under Auxiliary Effect of Dynamic Edges." Electronics 13, no. 10 (May 20, 2024): 1990. http://dx.doi.org/10.3390/electronics13101990.

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The scope of complex dynamical networks (CDNs) with dynamic edges is very wide, as it is composed of a class of realistic networks including web-winding systems, communication networks, neural networks, etc. However, a classic research topic in CDNs, the synchronization control problem, has not been effectively solved for CDNs with dynamic edges. This paper will investigate the emergence mechanism of synchronization from the perspective of large-scale systems. Firstly, a CDN with dynamic edges is conceptualized as an interconnected coupled system composed of an edge subsystem (ES) and a node subsystem (NS). Then, based on the proposed improved directed matrix ES model and expanded matrix inequality, this paper overcomes the limitations of coupling term design in node models and the strong correlation of tracking targets between nodes and edges. Due to the effect of the synthesized node controller and the auxiliary effect of the ES, state synchronization can be realized in the CDN. Finally, through simulation examples, the validity and advantages of our work compared to existing methods are demonstrated.

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Gao, Peitao, Yinhe Wang, Yi Peng, LiLi Zhang, and Shengping Li. "Tracking control of the nodes for the complex dynamical network with the auxiliary links dynamics." Information Sciences 628 (May 2023): 350–59. http://dx.doi.org/10.1016/j.ins.2023.01.124.

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Rubezic, Vesna, and Ana Jovanovic. "Erbium - doped fiber laser systems: Routes to chaos." Serbian Journal of Electrical Engineering 11, no. 4 (2014): 551–63. http://dx.doi.org/10.2298/sjee1404551r.

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Erbium-doped fiber laser systems exhibit a large variety of complex dynamical behaviors, bifurcations and attractors. In this paper, the chaotic behavior which can be achieved under certain conditions in a laser system with erbium-doped fiber, is discussed. The chaos in this system occurs through several standard scenarios. In this paper, the simulation sequence of quasiperiodic, intermittent and period-doubling scenario transitions to chaos is shown. Quasiperiodic and intermittent transitions to chaos are shown on the example system with a single ring. The electro-optical modulator was applied to the system for modulating the loss in the cavity. We used the sinusoidal and rectangular signals for modulation. Generation of chaos is achieved by changing the parameters of signal for modulation. Period-doubling transition to chaos is illustrated in a system with two rings. Simulation results are shown in the time domain and phase space.

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Gallas, Jason A. C. "Monogenic period equations are cyclotomic polynomials." International Journal of Modern Physics C 31, no. 04 (February 20, 2020): 2050058. http://dx.doi.org/10.1142/s0129183120500588.

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We study monogeneity in period equations, [Formula: see text], the auxiliary equations introduced by Gauss to solve cyclotomic polynomials by radicals. All monogenic [Formula: see text] of degrees [Formula: see text] are determined for extended intervals of primes [Formula: see text], and found to coincide either with cyclotomic polynomials or with simple de Moivre reduced forms of cyclotomic polynomials. The former case occurs for [Formula: see text], and the latter for [Formula: see text]. For [Formula: see text], we conjecture all monogenic period equations to be cyclotomic polynomials. Totally real period equations are of interest in applications of quadratic discrete-time dynamical systems.

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Ene, Remus-Daniel, Nicolina Pop, Marioara Lapadat, and Luisa Dungan. "Approximate Closed-Form Solutions for the Maxwell-Bloch Equations via the Optimal Homotopy Asymptotic Method." Mathematics 10, no. 21 (November 4, 2022): 4118. http://dx.doi.org/10.3390/math10214118.

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This paper emphasizes some geometrical properties of the Maxwell–Bloch equations. Based on these properties, the closed-form solutions of their equations are established. Thus, the Maxwell–Bloch equations are reduced to a nonlinear differential equation depending on an auxiliary unknown function. The approximate analytical solutions were built using the optimal homotopy asymptotic method (OHAM). These represent the ε-approximate OHAM solutions. A good agreement between the analytical and corresponding numerical results was found. The accuracy of the obtained results is validated through the representative figures. This procedure is suitable to be applied for dynamical systems with certain geometrical properties.

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Pieschner, Susanne, and Christiane Fuchs. "Bayesian inference for diffusion processes: using higher-order approximations for transition densities." Royal Society Open Science 7, no. 10 (October 2020): 200270. http://dx.doi.org/10.1098/rsos.200270.

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Modelling random dynamical systems in continuous time, diffusion processes are a powerful tool in many areas of science. Model parameters can be estimated from time-discretely observed processes using Markov chain Monte Carlo (MCMC) methods that introduce auxiliary data. These methods typically approximate the transition densities of the process numerically, both for calculating the posterior densities and proposing auxiliary data. Here, the Euler–Maruyama scheme is the standard approximation technique. However, the MCMC method is computationally expensive. Using higher-order approximations may accelerate it, but the specific implementation and benefit remain unclear. Hence, we investigate the utilization and usefulness of higher-order approximations in the example of the Milstein scheme. Our study demonstrates that the MCMC methods based on the Milstein approximation yield good estimation results. However, they are computationally more expensive and can be applied to multidimensional processes only with impractical restrictions. Moreover, the combination of the Milstein approximation and the well-known modified bridge proposal introduces additional numerical challenges.

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Nagarajan Krishnamurthy, Et al. "Heavy Vehicles: Distributed Hybrid Power System and Vehicle." International Journal on Recent and Innovation Trends in Computing and Communication 11, no. 1 (January 31, 2023): 185–88. http://dx.doi.org/10.17762/ijritcc.v11i1.9802.

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This research focuses on the development of a distributed hybrid power system and vehicle for heavy vehicles. The dynamical system comprises a power plant module, a drive module, an energy-storage module, and an entire car controller. The power plant module consists of one or more auxiliary power units that provide power to the heavy vehicle's power system. The drive module includes multiple driver elements responsible for directly driving the heavy vehicle's drive axles or operating individual wheels through direct drive. The energy-storage module serves as an energy reserve. The entire car controller is connected to the power plant module, drive module, and energy-storage module, enabling control over the activation of driver elements and the output of these elements to manage the heavy vehicle's transportation conditions. The novel approach eliminates the need for mechanical power transmission systems found in conventional engines and drive axles, allowing for flexible arrangement of auxiliary power units and driver elements on heavy vehicles.

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Xie, H., G. T. Flowers, L. Feng, and C. Lawrence. "Steady-State Dynamic Behavior of a Flexible Rotor With Auxiliary Support from a Clearance Bearing." Journal of Vibration and Acoustics 121, no. 1 (January 1, 1999): 78–83. http://dx.doi.org/10.1115/1.2893951.

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This paper investigates the steady-state responses of a rotor system supported by auxiliary bearings in which there is a clearance between the rotor and the inner race of the bearing. A simulation model based upon the rotor of a production jet engine is developed and its steady-state behavior is explored over a wide range of operating conditions for various parametric configurations. Specifically, the influence of rotor imbalance, clearance, support stiffness and damping is studied. Bifurcation diagrams are used as a tool to examine the dynamic behavior of this system as a function of the aforementioned parameters. The harmonic balance method is also employed for synchronous response cases. The observed dynamical responses is discussed and some insights into the behavior of such systems are presented.

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Liu, Lizhi, Cao Chen, Zilin Gao, and Bo Cheng. "Cluster synchronization for controlled nodes via the dynamics of edges in complex dynamical networks." PLOS ONE 18, no. 8 (August 3, 2023): e0288657. http://dx.doi.org/10.1371/journal.pone.0288657.

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An appropriate dynamic coupling form between nodes and edges’ state can effectively promote the emergence of desired network function (phenomenon), but the existing literatures have not conducted in-depth research on the coupling mechanism. This paper mainly focuses on the coupling auxiliary mechanism of dynamic edges for the emergence of cluster phenomenon of nodes, explores the essential relation between structure and function in complex dynamical networks (CDNs). Firstly, a novel model of CDNs has dynamic systems attached on not only nodes but also edges is proposed from the viewpoint of large-scale system. Secondly, a feedback nodes controller is synthesized associate with the designed linear and adaptive dynamics of edges. Via the appropriate dynamic behaviors of the edges system, the controlled nodes can realize cluster synchronized. Finally, the validity of the proposed approaches is verified by a given numerical example.

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Li, Yang, Qinghua Zhang, Yanwei Xu, Jinlong Wen, and Zhihao Wang. "Performance Evaluation of Inerter-Based Dynamic Vibration Absorbers for Wind-Induced Vibration Control of a Desulfurization Tower." Buildings 14, no. 1 (January 7, 2024): 150. http://dx.doi.org/10.3390/buildings14010150.

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High-rise flue gas desulfurization towers are susceptible to wind loads, which can cause instability and failure in the along-wind and across-wind directions. The tuned mass damper (TMD) has been widely applied in the wind-induced vibration control of high-rise structures. To enhance the control performance and reduce the auxiliary mass of TMD, this study focuses on inerter-based dynamic vibration absorbers (IDVAs) for controlling the vibration response of a desulfurization tower. The dynamical equations of the tower–IDVA systems are established under wind loads, and a parameter optimization strategy for IDVAs is proposed by using the genetic algorithm. The performance of the traditional TMD and six IDVAs in the vibration control of the tower are systematically compared. Numerical simulations demonstrate that both the TMD and IDVAs can substantially mitigate the vibration response of the tower. However, compared to the TMD with the same response mitigation ratio, more than 34% of the auxiliary mass can be reduced by two optimal IDVAs. In addition, the energy dissipation enhancement and lightweight effect of the two IDVAs are explained through parametric studies.

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Krishnan, Giri P., Gregory Filatov, Andrey Shilnikov, and Maxim Bazhenov. "Electrogenic properties of the Na+/K+ATPase control transitions between normal and pathological brain states." Journal of Neurophysiology 113, no. 9 (May 2015): 3356–74. http://dx.doi.org/10.1152/jn.00460.2014.

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Ionic concentrations fluctuate significantly during epileptic seizures. In this study, using a combination of in vitro electrophysiology, computer modeling, and dynamical systems analysis, we demonstrate that changes in the potassium and sodium intra- and extracellular ion concentrations ([K+] and [Na+], respectively) during seizure affect the neuron dynamics by modulating the outward Na+/K+pump current. First, we show that an increase of the outward Na+/K+pump current mediates termination of seizures when there is a progressive increase in the intracellular [Na+]. Second, we show that the Na+/K+pump current is crucial in maintaining the stability of the physiological network state; a reduction of this current leads to the onset of seizures via a positive-feedback loop. We then present a novel dynamical mechanism for bursting in neurons with a reduced Na+/K+pump. Overall, our study demonstrates the profound role of the current mediated by Na+/K+ATPase on the stability of neuronal dynamics that was previously unknown.

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Jansson, Olli, and Matthew W. Harris. "Convex Optimization-Based Techniques for Trajectory Design and Control of Nonlinear Systems with Polytopic Range." Aerospace 10, no. 1 (January 10, 2023): 71. http://dx.doi.org/10.3390/aerospace10010071.

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This paper presents new techniques for the trajectory design and control of nonlinear dynamical systems. The technique uses a convex polytope to bound the range of the nonlinear function and associates with each vertex an auxiliary linear system. Provided controls associated with the linear systems can be generated to satisfy an ordering constraint, the nonlinear control is computable by the interpolation of controls obtained by convex optimization. This theoretical result leads to two numerical approaches for solving the nonlinear constrained problem: one requires solving a single convex optimization problem and the other requires solving a sequence of convex optimization problems. The approaches are applied to two practical problems in aerospace engineering: a constrained relative orbital motion problem and an attitude control problem. The solve times for both problems and approaches are on the order of seconds. It is concluded that these techniques are rigorous and of practical use in solving nonlinear trajectory design and control problems.

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Gu, Mingxia, Zhiyong Yu, Haijun Jiang, and Da Huang. "Distributed consensus of discrete time-varying linear multi-agent systems with event-triggered intermittent control." Mathematical Biosciences and Engineering 21, no. 1 (2023): 415–43. http://dx.doi.org/10.3934/mbe.2024019.

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<abstract><p>The consensus problem of discrete time-varying linear multi-agent systems (MASs) is studied in this paper. First, an event-triggered intermittent control (ETIC) protocol is designed, aided by a class of auxiliary functions. Under this protocol, some sufficient conditions for all agents to achieve consensus are established by constructing an error dynamical system and applying the Lyapunov function. Second, in order to further reduce the communication burden, an improved event triggered intermittent control (I-ETIC) strategy is presented, along with corresponding convergence analysis. Notably, the difference between the two control protocols lies in the fact that the former protocol only determines when to control or not based on the trigger conditions, while the latter, building upon this, designs new event trigger conditions for the update of the controller during the control stage. Finally, two numerical simulation examples are provided to demonstrate the effectiveness of the theoretical results.</p></abstract>

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Klus, Stefan, Feliks Nüske, and Boumediene Hamzi. "Kernel-Based Approximation of the Koopman Generator and Schrödinger Operator." Entropy 22, no. 7 (June 30, 2020): 722. http://dx.doi.org/10.3390/e22070722.

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Many dimensionality and model reduction techniques rely on estimating dominant eigenfunctions of associated dynamical operators from data. Important examples include the Koopman operator and its generator, but also the Schrödinger operator. We propose a kernel-based method for the approximation of differential operators in reproducing kernel Hilbert spaces and show how eigenfunctions can be estimated by solving auxiliary matrix eigenvalue problems. The resulting algorithms are applied to molecular dynamics and quantum chemistry examples. Furthermore, we exploit that, under certain conditions, the Schrödinger operator can be transformed into a Kolmogorov backward operator corresponding to a drift-diffusion process and vice versa. This allows us to apply methods developed for the analysis of high-dimensional stochastic differential equations to quantum mechanical systems.

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Akhmet, Marat, Kaǧan Başkan, and Cihan Yeşil. "Delta synchronization of Poincaré chaos in gas discharge-semiconductor systems." Chaos: An Interdisciplinary Journal of Nonlinear Science 32, no. 8 (August 2022): 083137. http://dx.doi.org/10.1063/5.0103132.

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We introduce a new type of chaos synchronization, specifically the delta synchronization of Poincaré chaos. The method is demonstrated for the irregular dynamics in coupled gas discharge-semiconductor systems (GDSSs). It is remarkable that the processes are not generally synchronized. Our approach entirely relies on ingredients of the Poincaré chaos, which in its own turn is a consequence of the unpredictability in Poisson stable motions. The drive and response systems are in the connection, such that the latter is processed through the electric potential of the former. The absence of generalized synchronization between these systems is indicated by utilizing the conservative auxiliary system. However, the existence of common sequences of moments for finite convergence and separation confirms the delta synchronization. This can be useful for complex dynamics generation and control in electromagnetic devices. A bifurcation diagram is constructed to separate stable stationary solutions from non-trivial oscillatory ones. Phase portraits of the drive and response systems for a specific regime are provided. The results of the sequential test application to indicate the unpredictability and the delta synchronization of chaos are demonstrated in tables. The computations of the dynamical characteristics for GDSSs are carried out by using COMSOL Multiphysics version 5.6 and MATLAB version R2021b.

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Goncharenko, Borys, Larysa Vikhrova, and Mariia Miroshnichenko. "Optimal control of nonlinear stationary systems at infinite control time." Central Ukrainian Scientific Bulletin. Technical Sciences, no. 4(35) (2021): 88–93. http://dx.doi.org/10.32515/2664-262x.2021.4(35).88-93.

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The article presents a solution to the problem of control synthesis for dynamical systems described by linear differential equations that function in accordance with the integral-quadratic quality criterion under uncertainty. External perturbations, errors and initial conditions belong to a certain set of uncertainties. Therefore, the problem of finding the optimal control in the form of feedback on the output of the object is presented in the form of a minimum problem of optimal control under uncertainty. The problem of finding the optimal control and initial state, which maximizes the quality criterion, is considered in the framework of the optimization problem, which is solved by the method of Lagrange multipliers after the introduction of the auxiliary scalar function - Hamiltonian. The case of a stationary system on an infinite period of time is considered. The formulas that can be used for calculations are given for the first and second variations. It is proposed to solve the problem of control search in two stages: search of intermediate solution at fixed values of control and error vectors and subsequent search of final optimal control. The solution of -optimal control for infinite time taking into account the signal from the compensator output is also considered, as well as the solution of the corresponding matrix algebraic equations of Ricatti type.

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Camargo, Federico Gabriel. "Dynamic Modeling Of The Energy Returned On Invested." DYNA 89, no. 221 (April 26, 2022): 50–59. http://dx.doi.org/10.15446/dyna.v89n221.97965.

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This work was developed to present a conceptual and preliminary analysis of the concepts and criteria for estimating the Energy Return on Investment (EROI). In this work, methods based on monetary studies, Life Cycle Analysis (LCA) were discussed and a dynamical systems modeling was proposed. In this respect, we made a mathematical development, defining the state and auxiliary variables and the adjustment parameters necessary to study the problem. Some criteria and influencing factors were defined, in the medium and long term, the sustainability of the energy system and seek to incorporate them into relevant areas of discussion and education, encouraging their dissemination and reviews. It is sought to discuss the issues and considerations for a standardized methodology that allows comparisons and decision-making, in order to minimize environmental impact.

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Noor, Muhammad Aslam, Khalida Inayat Noor, and Michael Th Rassias. "New Trends in General Variational Inequalities." Acta Applicandae Mathematicae 170, no. 1 (October 6, 2020): 981–1064. http://dx.doi.org/10.1007/s10440-020-00366-2.

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Abstract It is well known that general variational inequalities provide us with a unified, natural, novel and simple framework to study a wide class of unrelated problems, which arise in pure and applied sciences. In this paper, we present a number of new and known numerical techniques for solving general variational inequalities and equilibrium problems using various techniques including projection, Wiener-Hopf equations, dynamical systems, the auxiliary principle and the penalty function. General variational-like inequalities are introduced and investigated. Properties of higher order strongly general convex functions have been discussed. The auxiliary principle technique is used to suggest and analyze some iterative methods for solving higher order general variational inequalities. Some new classes of strongly exponentially general convex functions are introduced and discussed. Our proofs of convergence are very simple as compared with other methods. Our results present a significant improvement of previously known methods for solving variational inequalities and related optimization problems. Since the general variational inequalities include (quasi) variational inequalities and (quasi) implicit complementarity problems as special cases, these results continue to hold for these problems. Some numerical results are included to illustrate the efficiency of the proposed methods. Several open problems have been suggested for further research in these areas.

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Elmandouh, Adel, Aqilah Aljuaidan, and Mamdouh Elbrolosy. "The Integrability and Modification to an Auxiliary Function Method for Solving the Strain Wave Equation of a Flexible Rod with a Finite Deformation." Mathematics 12, no. 3 (January 24, 2024): 383. http://dx.doi.org/10.3390/math12030383.

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Our study focuses on the governing equation of a finitely deformed flexible rod with strain waves. By utilizing the well-known Ablowita–Ramani–Segur (ARS) algorithm, we prove that the equation is non-integrable in the Painlevé sense. Based on the bifurcation theory for planar dynamical systems, we modify an auxiliary equation method to obtain a new systematic and effective method that can be used for a wide class of non-linear evolution equations. This method is summed up in an algorithm that explains and clarifies the ease of its applicability. The proposed method is successfully applied to construct wave solutions. The developed solutions are grouped as periodic, solitary, super periodic, kink, and unbounded solutions. A graphic representation of these solutions is presented using a 3D representation and a 2D representation, as well as a 2D contour plot.

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Kulagin, Anton E., and Alexander V. Shapovalov. "A Semiclassical Approach to the Nonlocal Nonlinear Schrödinger Equation with a Non-Hermitian Term." Mathematics 12, no. 4 (February 15, 2024): 580. http://dx.doi.org/10.3390/math12040580.

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The nonlinear Schrödinger equation (NLSE) with a non-Hermitian term is the model for various phenomena in nonlinear open quantum systems. We deal with the Cauchy problem for the nonlocal generalization of multidimensional NLSE with a non-Hermitian term. Using the ideas of the Maslov method, we propose the method of constructing asymptotic solutions to this equation within the framework of semiclassically concentrated states. The semiclassical nonlinear evolution operator and symmetry operators for the leading term of asymptotics are derived. Our approach is based on the solutions of the auxiliary dynamical system that effectively linearizes the problem under certain algebraic conditions. The formalism proposed is illustrated with the specific example of the NLSE with a non-Hermitian term that is the model of an atom laser. The analytical asymptotic solution to the Cauchy problem is obtained explicitly for this example.

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Wang, Xiaoming, Rimsha Ansar, Muhammad Abbas, Farah Aini Abdullah, and Khadijah M. Abualnaja. "The Investigation of Dynamical Behavior of Benjamin–Bona–Mahony–Burger Equation with Different Differential Operators Using Two Analytical Approaches." Axioms 12, no. 6 (June 16, 2023): 599. http://dx.doi.org/10.3390/axioms12060599.

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The dynamic behavior variation of the Benjamin–Bona–Mahony–Burger (BBM-Burger) equation has been investigated in this paper. The modified auxiliary equation method (MAEM) and Ricatti–Bernoulli (RB) sub-ODE method, two of the most reliable and useful analytical approaches, are used to construct soliton solutions for the proposed model. We demonstrate some of the extracted solutions using definitions of the β-derivative, conformable derivative (CD), and M-truncated derivatives (M-TD) to understand their dynamic behavior. The hyperbolic and trigonometric functions are used to derive the analytical solutions for the given model. As a consequence, dark, bell-shaped, anti-bell, M-shaped, W-shaped, kink soliton, and solitary wave soliton solutions are obtained. We observe the fractional parameter impact of the derivatives on physical phenomena. The BBM-Burger equation is functional in describing the propagation of long unidirectional waves in many nonlinear diffusive systems. The 2D and 3D graphs have been presented to confirm the behavior of analytical wave solutions.

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Guo, Liang, Shudi Liu, Litang Xi, Guofang Zhang, Ziqi Liu, Qi Zeng, Feipeng Lü, and Yuhong Wang. "Research on the Short-Term Economic Dispatch Method of Power System Involving a Hydropower-Photovoltaic-Pumped Storage Plant." Electronics 13, no. 7 (March 29, 2024): 1282. http://dx.doi.org/10.3390/electronics13071282.

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The auxiliary regulation capacity of pumped-storage power stations can be utilized as an effective method to regulate the output of a hydro-photovoltaic complementary system, further mitigating the power fluctuations of the system and enhancing the photovoltaic absorption. This study aims to minimize power fluctuations and maximize the economic benefits of electricity generation in a hydropower-photovoltaic-pumped-storage complementary system (HPPCS), which are treated as the objective functions. It explores the participation of the HPPCS in grid active power balance auxiliary services. By modulating the participation ratio of the HPPCS in the grid’s active balance service, the system output is aligned to fluctuate proportionally with the daily load curve trend. Consequently, a short-term economic dispatch model for the integrated HPPCS is developed. The case study focuses on the considerable impact of weather conditions on photovoltaic (PV) power generation. In this model, the outputs of cascading hydro-power stations and pumped-storage power stations are considered as the decision variables. A decomposition-based multi-objective evolutionary algorithm is applied to derive an optimized intra-day dispatch Pareto solution set for the cascading HPPCS in each of these scenarios. Additionally, this study compares the Pareto solution sets for the HPPCS in various extents of its participation in grid auxiliary services. The results of the case study suggest that the system is capable of timely adjustments during the peak and trough periods of load demand. Considering the economic benefits, it enables the pumped-storage station to generate electricity for the grid during periods of high electricity prices and to store energy by pumping water when prices are low.

Journal articles on the topic 'Auxiliary modulating dynamical systems'

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