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Добірка наукової літератури з теми "Nonlinear periodic systems"

Автор: Grafiati

Опубліковано: 19 жовтня 2024

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Статті в журналах з теми "Nonlinear periodic systems"

Gasiński, Leszek, and Nikolaos S. Papageorgiou. "Nonlinear Multivalued Periodic Systems." Journal of Dynamical and Control Systems 25, no. 2 (June 14, 2018): 219–43. http://dx.doi.org/10.1007/s10883-018-9408-9.

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Verriest, Erik I. "Balancing for Discrete Periodic Nonlinear Systems." IFAC Proceedings Volumes 34, no. 12 (August 2001): 249–54. http://dx.doi.org/10.1016/s1474-6670(17)34093-4.

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Luo, Albert C. J. "Periodic Flows to Chaos Based on Discrete Implicit Mappings of Continuous Nonlinear Systems." International Journal of Bifurcation and Chaos 25, no. 03 (March 2015): 1550044. http://dx.doi.org/10.1142/s0218127415500443.

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This paper presents a semi-analytical method for periodic flows in continuous nonlinear dynamical systems. For the semi-analytical approach, differential equations of nonlinear dynamical systems are discretized to obtain implicit maps, and a mapping structure based on the implicit maps is employed for a periodic flow. From mapping structures, periodic flows in nonlinear dynamical systems are predicted analytically and the corresponding stability and bifurcations of the periodic flows are determined through the eigenvalue analysis. The periodic flows predicted by the single-step implicit maps are discussed first, and the periodic flows predicted by the multistep implicit maps are also presented. Periodic flows in time-delay nonlinear dynamical systems are discussed by the single-step and multistep implicit maps. The time-delay nodes in discretization of time-delay nonlinear systems were treated by both an interpolation and a direct integration. Based on the discrete nodes of periodic flows in nonlinear dynamical systems with/without time-delay, the discrete Fourier series responses of periodic flows are presented. To demonstrate the methodology, the bifurcation tree of period-1 motion to chaos in a Duffing oscillator is presented as a sampled problem. The method presented in this paper can be applied to nonlinear dynamical systems, which cannot be solved directly by analytical methods.

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Can, Le Xuan. "On periodic waves of the nonlinear systems." Vietnam Journal of Mechanics 20, no. 4 (December 30, 1998): 11–19. http://dx.doi.org/10.15625/0866-7136/10037.

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The paper is concerned with the solvability and approximate solution of the nonlinear partial differential equation describing the periodic wave propagation. Necessary and sufficient conditions for the existence of the periodic wave solutions are obtained. An approximate method for solving the equation is presented. As an illustrative example, the equation of periodic waves of the electric cables is considered.

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Sundararajan, P., and S. T. Noah. "Dynamics of Forced Nonlinear Systems Using Shooting/Arc-Length Continuation Method—Application to Rotor Systems." Journal of Vibration and Acoustics 119, no. 1 (January 1, 1997): 9–20. http://dx.doi.org/10.1115/1.2889694.

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The analysis of systems subjected to periodic excitations can be highly complex in the presence of strong nonlinearities. Nonlinear systems exhibit a variety of dynamic behavior that includes periodic, almost-periodic (quasi-periodic), and chaotic motions. This paper describes a computational algorithm based on the shooting method that calculates the periodic responses of a nonlinear system under periodic excitation. The current algorithm calculates also the stability of periodic solutions and locates system parameter ranges where aperiodic and chaotic responses bifurcate from the periodic response. Once the system response for a parameter is known, the solution for near range of the parameter is calculated efficiently using a pseudo-arc length continuation procedure. Practical procedures for continuation, numerical difficulties and some strategies for overcoming them are also given. The numerical scheme is used to study the imbalance response of a rigid rotor supported on squeeze-film dampers and journal bearings, which have nonlinear stiffness and damping characteristics. Rotor spinning speed is used as the bifurcation parameter, and speed ranges of sub-harmonic, quasi-periodic and chaotic motions are calculated for a set of system parameters of practical interest. The mechanisms of these bifurcations also are explained through Floquet theory, and bifurcation diagrams.

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Ortega, Juan-Pablo. "Relative normal modes for nonlinear Hamiltonian systems." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 133, no. 3 (June 2003): 665–704. http://dx.doi.org/10.1017/s0308210500002602.

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An estimate on the number of distinct relative periodic orbits around a stable relative equilibrium in a Hamiltonian system with continuous symmetry is given. This result constitutes a generalization to the Hamiltonian symmetric framework of a classical result by Weinstein and Moser on the existence of periodic orbits in the energy levels surrounding a stable equilibrium. The estimate obtained is very precise in the sense that it provides a lower bound for the number of relative periodic orbits at each prescribed energy and momentum values neighbouring the stable relative equilibrium in question and with any prefixed (spatio-temporal) isotropy subgroup. Moreover, it is easily computable in particular examples. It is interesting to see how, in our result, the existence of non-trivial relative periodic orbits requires (generic) conditions on the higher-order terms of the Taylor expansion of the Hamiltonian function, in contrast with the purely quadratic requirements of the Weinstein–Moser theorem, which emphasizes the highly nonlinear character of the relatively periodic dynamical objects.

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Grigoraş, Victor, and Carmen Grigoraş. "Connecting Analog and Discrete Nonlinear Systems for Noise Generation." Bulletin of the Polytechnic Institute of Iași. Electrical Engineering, Power Engineering, Electronics Section 68, no. 1 (March 1, 2022): 81–90. http://dx.doi.org/10.2478/bipie-2022-0005.

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Abstract Nonlinear systems exhibit complex dynamic behaviour, including quasi-periodic and chaotic. The present contribution presents a composed analogue and discrete-time structure, based on second-order nonlinear building blocks with periodic oscillatory behaviour, that can be used for complex signal generation. The chosen feedback connection of the two modules aims at obtaining a more complex nonlinear dynamic behaviour than that of the building blocks. Performing a parameter scan, it is highlighted that the resulting nonlinear system has a quasi-periodic behaviour for large ranges of parameter values. The nonlinear system attractor projections are obtained by simulation and statistical numerical results are presented, both confirming the possible use of the designed system as a noise generator.

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Abbas, Saïd, Mouffak Benchohra, Soufyane Bouriah, and Juan J. Nieto. "Periodic solutions for nonlinear fractional differential systems." Differential Equations & Applications, no. 3 (2018): 299–316. http://dx.doi.org/10.7153/dea-2018-10-21.

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Kamenskii, Mikhail, Oleg Makarenkov, and Paolo Nistri. "Small parameter perturbations of nonlinear periodic systems." Nonlinearity 17, no. 1 (October 17, 2003): 193–205. http://dx.doi.org/10.1088/0951-7715/17/1/012.

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Ghadimi, M., A. Barari, H. D. Kaliji, and G. Domairry. "Periodic solutions for highly nonlinear oscillation systems." Archives of Civil and Mechanical Engineering 12, no. 3 (September 2012): 389–95. http://dx.doi.org/10.1016/j.acme.2012.06.014.

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Дисертації з теми "Nonlinear periodic systems"

Tang, Xiafei. "Periodic disturbance rejection of nonlinear systems." Thesis, University of Manchester, 2012. https://www.research.manchester.ac.uk/portal/en/theses/periodic-disturbance-rejection-of-nonlinear-systems(0bddefd9-2750-47fd-8c92-c90a01b8e1ef).html.

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Disturbance rejection is an important topic in control design since disturbances are inevitable in practical systems. To realise this target for nonlinear systems, this thesis brings in an assumption about the existence of a controlled invariant mani- fold and a Desired Feedforward Control (DFC) which is contained in the input to compensate the influence of disturbances. According to the approximation property of Neural Networks (NN) that any periodic signals defined in a compact set can be approximated by NN, the NN-based disturbance approximator is applied to approximate the DFC. Algorithmically, two important types of NN approximators that are Multi-layer Neural Networks (MNN) and Radial Basis Function Neural Networks (RBFNN) are presented in detail.In this thesis, a variety of nonlinear systems in standard canonical form are looked into. These forms are the output feedback form, the extended output feedback form, the decentralised output feedback form and the partial state feedback form. For these systems, four types of uncertainties are mainly considered. The first one is the disturbance that can be eliminated by the DFC. Secondly, the parameter uncertainty is taken into account. To get rid of this uncertainty, the adaptive control technique is employed for the estimation of unknown parameters, e.g. the NN gain matrix. The third one is the nonlinear uncertainty. For the case that nonlinear uncertainties are polynomials, it has a bound consisting of an unknown constant and a function of the regulated error such that this uncertainty can be also treated as the parameter uncertainty. Delay is the last type of uncertainty. Particularly, the delay is supposed to appear in output only. This uncertainty can be eliminated together with the nonlinear uncertainty. To establish the closed- loop stability, a Lyapunov-Krasovskii function is invoked. In addition, due to the requirement of the system structure or the stability analysis, some general control techniques are also involved such like the backstepping control and the high gain control.Throughout the results are illustrated by simulations.

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Abd-Elrady, Emad. "Nonlinear Approaches to Periodic Signal Modeling." Doctoral thesis, Uppsala : Acta Universitatis Upsaliensis : Univ.-bibl. [distributör], 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-4644.

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Groves, James O. "Small signal analysis of nonlinear systems with periodic operating trajectories." Diss., This resource online, 1995. http://scholar.lib.vt.edu/theses/available/etd-06062008-162614/.

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Zhang, Zhen. "Adaptive robust periodic output regulation." Columbus, Ohio : Ohio State University, 2007. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1187118803.

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Khames, Imene. "Nonlinear network wave equations : periodic solutions and graph characterizations." Thesis, Normandie, 2018. http://www.theses.fr/2018NORMIR04/document.

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Dans cette thèse, nous étudions les équations d’ondes non-linéaires discrètes dans des réseaux finis arbitraires. C’est un modèle général, où le Laplacien continu est remplacé par le Laplacien de graphe. Nous considérons une telle équation d’onde avec une non-linéarité cubique sur les nœuds du graphe, qui est le modèle φ4 discret, décrivant un réseau mécanique d’oscillateurs non-linéaires couplés ou un réseau électrique où les composantes sont des diodes ou des jonctions Josephson. L’équation d’onde linéaire est bien comprise en termes de modes normaux, ce sont des solutions périodiques associées aux vecteurs propres du Laplacien de graphe. Notre premier objectif est d’étudier la continuation des modes normaux dans le régime non-linéaire et le couplage des modes en présence de la non-linéarité. En inspectant les modes normaux du Laplacien de graphe, nous identifions ceux qui peuvent être étendus à des orbites périodiques non-linéaires. Il s’agit des modes normaux dont les vecteurs propres du Laplacien sont composés uniquement de {1}, {-1,+1} ou {-1,0,+1}. Nous effectuons systématiquement une analyse de stabilité linéaire (Floquet) de ces orbites et montrons le couplage des modes lorsque l’orbite est instable. Ensuite, nous caractérisons tous les graphes pour lesquels il existe des vecteurs propres du Laplacien ayant tous leurs composantes dans {-1,+1} ou {-1,0,+1}, en utilisant la théorie spectrale des graphes. Dans la deuxième partie, nous étudions des solutions périodiques localisées spatialement. En supposant une condition initiale de grande amplitude localisée sur un nœud du graphe, nous approchons l’évolution du système par l’équation de Duffing pour le nœud excité et un système linéaire forcé pour le reste du réseau. Cette approximation est validée en réduisant l’équation φ4 discrète à l’équation de Schrödinger non-linéaire de graphes et par l’analyse de Fourier de la solution numérique. Les résultats de cette thèse relient la dynamique non-linéaire à la théorie spectrale des graphes
In this thesis, we study the discrete nonlinear wave equations in arbitrary finite networks. This is a general model, where the usual continuum Laplacian is replaced by the graph Laplacian. We consider such a wave equation with a cubic on-site nonlinearity which is the discrete φ4 model, describing a mechanical network of coupled nonlinear oscillators or an electrical network where the components are diodes or Josephson junctions. The linear graph wave equation is well understood in terms of normal modes, these are periodic solutions associated to the eigenvectors of the graph Laplacian. Our first goal is to investigate the continuation of normal modes in the nonlinear regime and the modes coupling in the presence of nonlinearity. By inspecting the normal modes of the graph Laplacian, we identify which ones can be extended into nonlinear periodic orbits. They are normal modes whose Laplacian eigenvectors are composed uniquely of {1}, {-1,+1} or {-1,0,+1}. We perform a systematic linear stability (Floquet) analysis of these orbits and show the modes coupling when the orbit is unstable. Then, we characterize all graphs for which there are eigenvectors of the graph Laplacian having all their components in {-1,+1} or {-1,0,+1}, using graph spectral theory. In the second part, we investigate periodic solutions that are spatially localized. Assuming a large amplitude localized initial condition on one node of the graph, we approximate its evolution by the Duffing equation. The rest of the network satisfies a linear system forced by the excited node. This approximation is validated by reducing the discrete φ4 equation to the graph nonlinear Schrödinger equation and by Fourier analysis. The results of this thesis relate nonlinear dynamics to graph spectral theory

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Warkomski, Edward Joseph 1958. "Nonlinear structures subject to periodic and random vibration with applications to optical systems." Thesis, The University of Arizona, 1990. http://hdl.handle.net/10150/277811.

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The methods for analysis of a three degree-of-freedom nonlinear optical support system, subject to periodic and random vibration, are presented. The analysis models were taken from those generated for the dynamic problems related to the NASA Space Infrared Telescope Facility (SIRTF). The models treat the one meter, 116 kilogram (258 pound) primary mirror of the SIRTF as a rigid mass, with elastic elements representing the mirror support structure. Both linear and nonlinear elastic supports are evaluated for the SIRTF. Advanced Continuous Simulation Language (ACSL), a commercially available software package for numerical solution of nonlinear, time-dependent differential equations, was used for all models. The methods presented for handling the nonlinear differential equations can be readily adapted for handling other similar dynamics problems.

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Zhang, Xiaohong. "Optimal feedback control for nonlinear discrete systems and applications to optimal control of nonlinear periodic ordinary differential equations." Diss., Virginia Tech, 1993. http://hdl.handle.net/10919/40185.

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Myers, Owen Dale. "Spatiotemporally Periodic Driven System with Long-Range Interactions." ScholarWorks @ UVM, 2015. http://scholarworks.uvm.edu/graddis/524.

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It is well known that some driven systems undergo transitions when a system parameter is changed adiabatically around a critical value. This transition can be the result of a fundamental change in the structure of the phase space, called a bifurcation. Most of these transitions are well classified in the theory of bifurcations. Among the driven systems, spatiotemporally periodic (STP) potentials are noteworthy due to the intimate coupling between their time and spatial components. A paradigmatic example of such a system is the Kapitza pendulum, which is a pendulum with an oscillating suspension point. The Kapitza pendulum has the strange property that it will stand stably in the inverted position for certain driving frequencies and amplitudes. A particularly interesting and useful STP system is an array of parallel electrodes driven with an AC electrical potential such that adjacent electrodes are 180 degrees out of phase. Such an electrode array embedded in a surface is called an Electric Curtain (EC). As we will show, by using two ECs and a quadrupole trap it is posible to produce an electric potential simular in form to that of the Kapitza pendulum. Here I will present the results of four related pieces of work, each focused on understanding the behaviors STP systems, long-range interacting particles, and long-range interacting particles in STP systems. I will begin with a discussion on the experimental results of the EC as applied to the cleaning of solar panels in extraterrestrial environments, and as a way to produce a novel one-dimensional multiparticle STP potential. Then I will present a numerical investigation and dynamical systems analysis of the dynamics that may be possible in an EC. Moving to a simpler model in order to explore the rudimentary physics of coulomb interactions in a STP potential, I will show that the tools of statistical mechanics may be important to the study of such systems to understand transitions that fall outside of bifurcation theory. Though the Coulomb and, similarly, gravitational interactions of particles are prevalent in nature, these long-range interactions are not well understood from a statistical mechanics perspective because they are not extensive or additive. Finally, I will present a simple model for understanding long-range interacting pendula, finding interesting non-equilibrium behavior of the pendula angles. Namely, that a quasistationary clustered state can exist when the angles are initially ordered by their index.

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Hayward, Peter J. "On the computation of periodic responses for nonlinear dynamic systems with multi-harmonic forcing." Thesis, University of Sussex, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.429733.

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Royston, Thomas James. "Computational and Experimental Analyses of Passive and Active, Nonlinear Vibration Mounting Systems Under Periodic Excitation /." The Ohio State University, 1995. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487928649987553.

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Книги з теми "Nonlinear periodic systems"

Reithmeier, Eduard. Periodic Solutions of Nonlinear Dynamical Systems. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/bfb0094521.

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Chulaevskiĭ, V. A. Almost periodic operators and related nonlinear integrable systems. Manchester, UK: Manchester University Press, 1989.

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Ambrosetti, A. Periodic solutions of singular Lagrangian systems. Boston: Birkhäuser, 1993.

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author, Bolle Philippe, ed. Quasi-periodic solutions of nonlinear wave equations in the D-dimensional torus. Berlin: European Mathematical Society, 2020.

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Reithmeier, Eduard. Periodic solutions of nonlinear dynamical systems: Numerical computation, stability, bifurcation, and transition to chaos. Berlin: Springer-Verlag, 1991.

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P, Walker K., and United States. National Aeronautics and Space Administration., eds. Nonlinear mesomechanics of composites with periodic microstructure: Final report on NASA NAG3-882. [Washington, DC]: National Aeronautics and Space Administration, 1991.

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Fiedler, Bernold. Global bifurcation of periodic solutions with symmetry. Berlin: Springer-Verlag, 1988.

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Luo, Albert C. J. Periodic Flows to Chaos in Time-delay Systems. Springer, 2016.

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Chulaevsky, V. A. Almost Periodic Operators and Related Nonlinear Integrable Systems (Nonlinear Science: Theory & Application). John Wiley & Sons, 1992.

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Coti-Zelati, V., and A. Ambrosetti. Periodic Solutions of Singular Lagrangian Systems. Birkhauser Verlag, 2012.

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Частини книг з теми "Nonlinear periodic systems"

Toda, Morikazu. "Periodic Systems." In Theory of Nonlinear Lattices, 98–146. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-642-83219-2_4.

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Luo, Albert C. J. "Periodic Flows in Continuous Systems." In Nonlinear Physical Science, 199–279. Berlin, Heidelberg: Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-662-47275-0_5.

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Szemplińska-Stupnicka, Wanda. "Secondary Resonances (Periodic and Almost-Periodic)." In The Behavior of Nonlinear Vibrating Systems, 171–245. Dordrecht: Springer Netherlands, 1990. http://dx.doi.org/10.1007/978-94-009-1870-2_7.

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Akhmet, Marat. "Discontinuous Almost Periodic Functions." In Nonlinear Systems and Complexity, 69–84. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-20572-0_3.

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Akhmet, Marat. "Discontinuous Almost Periodic Solutions." In Nonlinear Systems and Complexity, 85–101. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-20572-0_4.

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Anishchenko, Vadim S., Tatyana E. Vadivasova, and Galina I. Strelkova. "Synchronization of Periodic Self-Sustained Oscillations." In Deterministic Nonlinear Systems, 217–43. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-06871-8_13.

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Belyakov, Vladimir Alekseevich. "Nonlinear Optics of Periodic Media." In Partially Ordered Systems, 188–214. New York, NY: Springer New York, 1992. http://dx.doi.org/10.1007/978-1-4612-4396-0_6.

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Akhmet, Marat. "Periodic Solutions of Nonlinear Systems." In Principles of Discontinuous Dynamical Systems, 99–111. New York, NY: Springer New York, 2010. http://dx.doi.org/10.1007/978-1-4419-6581-3_7.

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Luo, Albert C. J. "Periodic Flows in Time-delay Systems." In Nonlinear Systems and Complexity, 221–70. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-42778-2_4.

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Luo, Albert C. J. "Periodic Flows in Time-Delay Systems." In Nonlinear Systems and Complexity, 81–113. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-42664-8_3.

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Тези доповідей конференцій з теми "Nonlinear periodic systems"

Sukhorukov, Andrey A., N. Marsal, A. Minovich, D. Wolfersberger, M. Sciamanna, G. Montemezzani, D. N. Neshev, and Yu S. Kivshar. "Control of modulational instability in periodic feedback systems." In Nonlinear Photonics. Washington, D.C.: OSA, 2010. http://dx.doi.org/10.1364/np.2010.nmd7.

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Shermeneva, Maria. "Nonlinear periodic waves on a slope." In Modeling complex systems. AIP, 2001. http://dx.doi.org/10.1063/1.1386843.

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Vakakis, Alexander. "Nonlinear Periodic Systems: Bands and Localization." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-87315.

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We consider the dynamics of nonlinear mono-coupled periodic media. When coupling dominates over nonlinearity near-field standing waves and spatially extended traveling waves exist, inside stop and pass bands, respectively, of the nonlinear system. Nonlinear standing waves are analytically studied using a nonlinear normal mode formulation, whereas nonlinear traveling waves are analyzed by the method of multiple scales. When the nonlinear effects are of the same order with the coupling ones a completely different picture emerges, since nonlinear resonance interactions are unavoidable. As a result, infinite families of strongly and weakly localized nonlinear standing waves appear with frequencies lying in pass or stop bands of the corresponding linear periodic medium. Moreover, in the limit of weak coupling these solutions develop sensitive dependence on initial conditions, and the possibility of spatial chaos in the system exists. Some additional results on chaotic dynamics in linear periodic media with strongly nonlinear disorders are reviewed.

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Vladimirov, A. G., E. B. Pelyukhova, and E. E. Fradkin. "Periodic and Chaotic Operations of a Laser with a Saturable Absorber." In Nonlinear Dynamics in Optical Systems. Washington, D.C.: Optica Publishing Group, 1990. http://dx.doi.org/10.1364/nldos.1990.oc527.

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We study numerically and analytically the small amplitude periodic solutions of semiclassical equations for a laser with a saturable absorber. We investigate the bifurcation sequence, leading to period-doublings, crises of chaotic attractors, and intermittency.

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Mandel, Paul, N. P. Pettiaux, Wang Kaige, P. Galatola, and L. A. Lugiato. "Generic Properties of Periodic Attractors in Two-Photon Processes." In Nonlinear Dynamics in Optical Systems. Washington, D.C.: Optica Publishing Group, 1990. http://dx.doi.org/10.1364/nldos.1990.ob257.

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We show that the periodic attractors occurring in two-photon processes displaying a phase instability have common properties including a domain of hysteresis. The case of degenerate four-wave mixing includes also some nongeneric attractors which exhibit a Berry phase phenomenon.

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Winful, Herbert G., Shawe-Shiuan Wang, and Richard K. DeFreez. "Periodic and Chaotic Beam Scanning in Semiconductor Laser Arrays." In Nonlinear Dynamics in Optical Systems. Washington, D.C.: Optica Publishing Group, 1990. http://dx.doi.org/10.1364/nldos.1990.pdp4.

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Winful, Herbert G., Shawe-Shiuan Wang, and Richard K. DcFreez. "Spontaneous Periodic and Chaotic Beam Scanning in Semiconductor Laser Arrays." In Nonlinear Dynamics in Optical Systems. Washington, D.C.: Optica Publishing Group, 1990. http://dx.doi.org/10.1364/nldos.1990.sdslad119.

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De Jagher, P. C., and D. Lenstra. "The modulated semiconductor laser: a Hamiltonian search for its periodic attractors." In Nonlinear Dynamics in Optical Systems. Washington, D.C.: Optica Publishing Group, 1992. http://dx.doi.org/10.1364/nldos.1992.tha5.

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Modulated lasers have been investigated for over a decade now, c.f. ref. [3] and references cited therein. Periodic as well as chaotic types of operation have been observed. In this paper we put forward a mathematical technique to calculate lower and upper bounds for the modulation strength which is needed to sustain a periodic large amplitude output.

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Pettiaux, Nicolas, and Thomas Erneux. "From harmonic to pulsating periodic solutions in intracavity second harmonic generation." In Nonlinear Dynamics in Optical Systems. Washington, D.C.: Optica Publishing Group, 1992. http://dx.doi.org/10.1364/nldos.1992.mc25.

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We consider the problem of Second Harmonic Generation (SHG) inside a resonant cavity, pumped by an external laser. The elementary process that takes place in SHG is the absorption of 2 photons of frequency ω and the emission of one photon at frequency 2ω. Drummond et al[1] have shown that this problem can be modeled by two ordinary differential equations for the (complex) amplitudes of the electrical fields: where overbar means complex conjugate.

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Royston, Thomas J., and Rajendra Singh. "Periodic Response of Nonlinear Engine Mounting Systems." In SAE Noise and Vibration Conference and Exposition. 400 Commonwealth Drive, Warrendale, PA, United States: SAE International, 1995. http://dx.doi.org/10.4271/951297.

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Звіти організацій з теми "Nonlinear periodic systems"

Mirus, Kevin A. Control of nonlinear systems using periodic parametric perturbations with application to a reversed field pinch. Office of Scientific and Technical Information (OSTI), January 1998. http://dx.doi.org/10.2172/656820.

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Soloviev, Vladimir, and Andrey Belinskij. Methods of nonlinear dynamics and the construction of cryptocurrency crisis phenomena precursors. [б. в.], 2018. http://dx.doi.org/10.31812/123456789/2851.

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This article demonstrates the possibility of constructing indicators of critical and crisis phenomena in the volatile market of cryptocurrency. For this purpose, the methods of the theory of complex systems such as recurrent analysis of dynamic systems and the calculation of permutation entropy are used. It is shown that it is possible to construct dynamic measures of complexity, both recurrent and entropy, which behave in a proper way during actual pre-crisis periods. This fact is used to build predictors of crisis phenomena on the example of the main five crises recorded in the time series of the key cryptocurrency bitcoin, the effectiveness of the proposed indicators-precursors of crises has been identified.

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Moon, Francis C. Nonlinear dynamics of fluid-structure systems. Final technical report for period January 5, 1991 - December 31, 1997. Office of Scientific and Technical Information (OSTI), July 1999. http://dx.doi.org/10.2172/756804.

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Bielinskyi, Andrii O., Oleksandr A. Serdyuk, Сергій Олексійович Семеріков, Володимир Миколайович Соловйов, Андрій Іванович Білінський, and О. А. Сердюк. Econophysics of cryptocurrency crashes: a systematic review. Криворізький державний педагогічний університет, December 2021. http://dx.doi.org/10.31812/123456789/6974.

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Cryptocurrencies refer to a type of digital asset that uses distributed ledger, or blockchain technology to enable a secure transaction. Like other financial assets, they show signs of complex systems built from a large number of nonlinearly interacting constituents, which exhibits collective behavior and, due to an exchange of energy or information with the environment, can easily modify its internal structure and patterns of activity. We review the econophysics analysis methods and models adopted in or invented for financial time series and their subtle properties, which are applicable to time series in other disciplines. Quantitative measures of complexity have been proposed, classified, and adapted to the cryptocurrency market. Their behavior in the face of critical events and known cryptocurrency market crashes has been analyzed. It has been shown that most of these measures behave characteristically in the periods preceding the critical event. Therefore, it is possible to build indicators-precursors of crisis phenomena in the cryptocurrency market.

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Wu, Yingjie, Selim Gunay, and Khalid Mosalam. Hybrid Simulations for the Seismic Evaluation of Resilient Highway Bridge Systems. Pacific Earthquake Engineering Research Center, University of California, Berkeley, CA, November 2020. http://dx.doi.org/10.55461/ytgv8834.

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Bridges often serve as key links in local and national transportation networks. Bridge closures can result in severe costs, not only in the form of repair or replacement, but also in the form of economic losses related to medium- and long-term interruption of businesses and disruption to surrounding communities. In addition, continuous functionality of bridges is very important after any seismic event for emergency response and recovery purposes. Considering the importance of these structures, the associated structural design philosophy is shifting from collapse prevention to maintaining functionality in the aftermath of moderate to strong earthquakes, referred to as “resiliency” in earthquake engineering research. Moreover, the associated construction philosophy is being modernized with the utilization of accelerated bridge construction (ABC) techniques, which strive to reduce the impact of construction on traffic, society, economy and on-site safety. This report presents two bridge systems that target the aforementioned issues. A study that combined numerical and experimental research was undertaken to characterize the seismic performance of these bridge systems. The first part of the study focuses on the structural system-level response of highway bridges that incorporate a class of innovative connecting devices called the “V-connector,”, which can be used to connect two components in a structural system, e.g., the column and the bridge deck, or the column and its foundation. This device, designed by ACII, Inc., results in an isolation surface at the connection plane via a connector rod placed in a V-shaped tube that is embedded into the concrete. Energy dissipation is provided by friction between a special washer located around the V-shaped tube and a top plate. Because of the period elongation due to the isolation layer and the limited amount of force transferred by the relatively flexible connector rod, bridge columns are protected from experiencing damage, thus leading to improved seismic behavior. The V-connector system also facilitates the ABC by allowing on-site assembly of prefabricated structural parts including those of the V-connector. A single-column, two-span highway bridge located in Northern California was used for the proof-of-concept of the proposed V-connector protective system. The V-connector was designed to result in an elastic bridge response based on nonlinear dynamic analyses of the bridge model with the V-connector. Accordingly, a one-third scale V-connector was fabricated based on a set of selected design parameters. A quasi-static cyclic test was first conducted to characterize the force-displacement relationship of the V-connector, followed by a hybrid simulation (HS) test in the longitudinal direction of the bridge to verify the intended linear elastic response of the bridge system. In the HS test, all bridge components were analytically modeled except for the V-connector, which was simulated as the experimental substructure in a specially designed and constructed test setup. Linear elastic bridge response was confirmed according to the HS results. The response of the bridge with the V-connector was compared against that of the as-built bridge without the V-connector, which experienced significant column damage. These results justified the effectiveness of this innovative device. The second part of the study presents the HS test conducted on a one-third scale two-column bridge bent with self-centering columns (broadly defined as “resilient columns” in this study) to reduce (or ultimately eliminate) any residual drifts. The comparison of the HS test with a previously conducted shaking table test on an identical bridge bent is one of the highlights of this study. The concept of resiliency was incorporated in the design of the bridge bent columns characterized by a well-balanced combination of self-centering, rocking, and energy-dissipating mechanisms. This combination is expected to lead to minimum damage and low levels of residual drifts. The ABC is achieved by utilizing precast columns and end members (cap beam and foundation) through an innovative socket connection. In order to conduct the HS test, a new hybrid simulation system (HSS) was developed, utilizing commonly available software and hardware components in most structural laboratories including: a computational platform using Matlab/Simulink [MathWorks 2015], an interface hardware/software platform dSPACE [2017], and MTS controllers and data acquisition (DAQ) system for the utilized actuators and sensors. Proper operation of the HSS was verified using a trial run without the test specimen before the actual HS test. In the conducted HS test, the two-column bridge bent was simulated as the experimental substructure while modeling the horizontal and vertical inertia masses and corresponding mass proportional damping in the computer. The same ground motions from the shaking table test, consisting of one horizontal component and the vertical component, were applied as input excitations to the equations of motion in the HS. Good matching was obtained between the shaking table and the HS test results, demonstrating the appropriateness of the defined governing equations of motion and the employed damping model, in addition to the reliability of the developed HSS with minimum simulation errors. The small residual drifts and the minimum level of structural damage at large peak drift levels demonstrated the superior seismic response of the innovative design of the bridge bent with self-centering columns. The reliability of the developed HS approach motivated performing a follow-up HS study focusing on the transverse direction of the bridge, where the entire two-span bridge deck and its abutments represented the computational substructure, while the two-column bridge bent was the physical substructure. This investigation was effective in shedding light on the system-level performance of the entire bridge system that incorporated innovative bridge bent design beyond what can be achieved via shaking table tests, which are usually limited by large-scale bridge system testing capacities.

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