Готові списки джерел за темами / Differential system state equations

Добірка наукової літератури з теми "Differential system state equations"

Автор: Grafiati
Опубліковано: 30 травня 2022
Оновлено: 31 травня 2022

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Статті в журналах з теми "Differential system state equations"

1

Tukhtasinov, Muminjon, Gafurjan Ibragimov, Sarvinoz Kuchkarova, and Risman Mat Hasim. "Differential Games for an Infinite 2-Systems of Differential Equations." Mathematics 9, no. 13 (June 23, 2021): 1467. http://dx.doi.org/10.3390/math9131467.

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Анотація:
A pursuit differential game described by an infinite system of 2-systems is studied in Hilbert space l2. Geometric constraints are imposed on control parameters of pursuer and evader. The purpose of pursuer is to bring the state of the system to the origin of the Hilbert space l2 and the evader tries to prevent this. Differential game is completed if the state of the system reaches the origin of l2. The problem is to find a guaranteed pursuit and evasion times. We give an equation for the guaranteed pursuit time and propose an explicit strategy for the pursuer. Additionally, a guaranteed evasion time is found.
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2

Trigeassou, Jean-Claude, and Nezha Maamri. "Optimal State Control of Fractional Order Differential Systems: The Infinite State Approach." Fractal and Fractional 5, no. 2 (April 5, 2021): 29. http://dx.doi.org/10.3390/fractalfract5020029.

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Optimal control of fractional order systems is a long established domain of fractional calculus. Nevertheless, it relies on equations expressed in terms of pseudo-state variables which raise fundamental questions. So in order remedy these problems, the authors propose in this paper a new and original approach to fractional optimal control based on a frequency distributed representation of fractional differential equations called the infinite state approach, associated with an original formulation of fractional energy, which is intended to really control the internal system state. In the first step, the fractional calculus of variations is revisited to express appropriate Euler Lagrange equations. Then, the quadratic optimal control of fractional linear systems is formulated. Thanks to a frequency discretization technique, the previous theoretical equations are converted into an equivalent large dimension integer order system which permits the implementation of a feasible optimal solution. A numerical example illustrates the validity of this new approach.
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3

JIANG, YAO-LIN. "STEADY-STATE METHODS OF DIFFERENTIAL-ALGEBRAIC EQUATIONS IN CIRCUIT SIMULATION." Journal of Circuits, Systems and Computers 14, no. 02 (April 2005): 383–93. http://dx.doi.org/10.1142/s0218126605002313.

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Анотація:
In the paper, we study the steady-state methods of large dynamic systems. For a nonlinear system of differential-algebraic equations with a known period T, we decouple it, in function space, into linear subsystems by quasilinearization. The resulting linear dynamic systems can be solved by a waveform Krylov subspace method. For the autonomous case, that is, the period T is unknown, the well-known shooting process can be applied where Newton iterations are computed with pseudo-inverse.
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4

GREENBAUN, N. N. "THE MARGINAL STABILITY OF AUTONOMOUS DIFFERENTIAL EQUATIONS." International Journal of Bifurcation and Chaos 03, no. 03 (June 1993): 785–88. http://dx.doi.org/10.1142/s0218127493000702.

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Анотація:
Solutions in the vicinity of a steady state solution to a system of autonomous nonlinear differential equations are of interest to modelers. The usual method for determining marginal stability of the steady state is the Routh-Hurwitz criterion. The method offered here is less complicated and more efficient when the number of state variables exceeds three.
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5

Ibănescu, M., and R. Ibănescu. "New approach in solving derivative causality problems in the bond-graph method." IOP Conference Series: Materials Science and Engineering 1235, no. 1 (March 1, 2022): 012053. http://dx.doi.org/10.1088/1757-899x/1235/1/012053.

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Анотація:
Abstract From the bond-graph model of a dynamic system, the state equations can be obtained. When the system contains only energy storing elements in integral causality, the system of state equations is immediately and directly determined. When the model contains at least one energy storing element in derivative causality, the resulted system of differential-algebraic equations arises some difficulties in finding the final form of the system of state equations. The work presents a new method of deducing the state equations in case of bond-graph models with one, or several energy storing elements in derivative causality. This method is based on the kinetic energy of the system and offers the possibility to avoid a difficult mathematical calculus for the transition from a system of differential algebraic equations to the system of state equations.
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6

Chen, Xiaopeng, and Jinqiao Duan. "State space decomposition for non-autonomous dynamical systems." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 141, no. 5 (September 26, 2011): 957–74. http://dx.doi.org/10.1017/s0308210510000661.

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Анотація:
The decomposition of state spaces into dynamically different components is helpful for understanding dynamics of complex systems. A Conley-type decomposition theorem is proved for non-autonomous dynamical systems defined on a non-compact but separable state space. Specifically, the state space can be decomposed into a chain-recurrent part and a gradient-like part. This result applies to both non-autonomous ordinary differential equations on a Euclidean space (which is only locally compact), and to non-autonomous partial differential equations on an infinite-dimensional function space (which is not even locally compact). This decomposition result is demonstrated by discussing a few concrete examples, such as the Lorenz system and the Navier–Stokes system, under time-dependent forcing.
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7

Zawadzki, Andrzej. "Application of local coordinates rectification in linearization of selected parameters of dynamic nonlinear systems." COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering 33, no. 5 (August 26, 2014): 1819–30. http://dx.doi.org/10.1108/compel-11-2013-0358.

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Анотація:
Purpose – The purpose of this paper is to aim to an application of element of the theory of differential geometry for building the state space transformation, linearizing nonlinear dynamic system into a linear form. Design/methodology/approach – It is assumed that the description of nonlinear electric circuits with concentrated parameters or electromechanical systems is given by nonlinear system of differential equations of first order (state equations). The goal is to find transformation which leads nonlinear state equation (written in one coordinate system) to the linear in the other – sought coordinate system. Findings – The necessary conditions fulfilled by nonlinear system undergoing linearization process are presented. Numerical solutions of the nonlinear equations of state together with linearized system obtained from direct transformation of the state space are included (transformation input – the state of the nonlinear system). Originality/value – Application of first order exact differential forms for determining the transformation linearizing the nonlinear state equation. Simple linear models obtained with the use of the linearizing transformation are very useful (mainly because of the known and well-mastered theory of linear systems) in solving of various practical technical problems.
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8

Zhu, Qingfeng, Yufeng Shi, Jiaqiang Wen, and Hui Zhang. "A Type of Time-Symmetric Stochastic System and Related Games." Symmetry 13, no. 1 (January 12, 2021): 118. http://dx.doi.org/10.3390/sym13010118.

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Анотація:
This paper is concerned with a type of time-symmetric stochastic system, namely the so-called forward–backward doubly stochastic differential equations (FBDSDEs), in which the forward equations are delayed doubly stochastic differential equations (SDEs) and the backward equations are anticipated backward doubly SDEs. Under some monotonicity assumptions, the existence and uniqueness of measurable solutions to FBDSDEs are obtained. The future development of many processes depends on both their current state and historical state, and these processes can usually be represented by stochastic differential systems with time delay. Therefore, a class of nonzero sum differential game for doubly stochastic systems with time delay is studied in this paper. A necessary condition for the open-loop Nash equilibrium point of the Pontriagin-type maximum principle are established, and a sufficient condition for the Nash equilibrium point is obtained. Furthermore, the above results are applied to the study of nonzero sum differential games for linear quadratic backward doubly stochastic systems with delay. Based on the solution of FBDSDEs, an explicit expression of Nash equilibrium points for such game problems is established.
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9

Klamka, J., A. Babiarz, and M. Niezabitowski. "Banach fixed-point theorem in semilinear controllability problems – a survey." Bulletin of the Polish Academy of Sciences Technical Sciences 64, no. 1 (March 1, 2016): 21–35. http://dx.doi.org/10.1515/bpasts-2016-0004.

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Анотація:
Abstract The main aim of this article is to review the existing state of art concerning the complete controllability of semilinear dynamical systems. The study focus on obtaining the sufficient conditions for the complete controllability for various systems using the Banach fixedpoint theorem. We describe the results for stochastic semilinear functional integro-differential system, stochastic partial differential equations with finite delays, semilinear functional equations, a stochastic semilinear system, a impulsive stochastic integro-differential system, semilinear stochastic impulsive systems, an impulsive neutral functional evolution integro-differential system and a nonlinear stochastic neutral impulsive system. Finally, two examples are presented.
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10

Glagolev, Mikhail V., Aleksandr F. Sabrekov, and Vladimir M. Goncharov. "Delay differential equations as a tool for mathematical modelling of population dynamic." Environmental Dynamics and Global Climate Change 9, no. 2 (November 27, 2018): 40–63. http://dx.doi.org/10.17816/edgcc10483.

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Анотація:
The manuscript constitutes a lecture from a course “Mathematical modelling of biological processes”, adapted to the format of the journal paper. This course of lectures is held by one of authors in Ugra State University. Delay differential equations are widely used in different ecological and biological problems. It has to do with the fact that delay differential equations are able to take into account that different biological processes depend not only on the state of the system at the moment but on the state of the system in previous moments too. The most popular case of using delay differential equations in biology is modelling in population ecology (including the modelling of several interacting populations dynamic, for example, in predator-prey system). Also delay differential equations are considered in demography, immunology, epidemiology, molecular biology (to provide mathematical description of regulatory mechanisms in a cell functioning and division), physiology as well as for modelling certain important production processes (for example, in agriculture). In the beginning of the paper as introduction some basic concepts of differential difference equation theory (delay differential equations are specific type of differential difference equations) is considered and their classification is presented. Then it is discussed in more detail how such an important equations of population dynamic as Maltus equation and logistic (Verhulst-Pearl) equation are transformed into corresponsive delay differential equations – Goudriaan-Roermund and Hutchinson. Then several discussion questions on using of a delay differential equations in biological models are considered. It is noted that in a certain cases using of a delay differential equations lead to an incorrect behavior from the point of view of common sense. Namely solution of Goudriaan-Roermund equation with harvesting, stopped when all species were harvested, shows that spontaneous generation takes place in the system. This incorrect interpretation has to do with the fact that delay differential equations are used to simplify considered models (that are usually are systems of ordinary differential equations). Using of integro-differential equations could be more appropriate because in these equations background could be taken into account in a more natural way. It is shown that Hutchinson equation can be obtained by simplification of Volterra integral equation with a help of Diraq delta function. Finally, a few questions of analytical and numerical solution of delay differential equations are discussed.
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Дисертації з теми "Differential system state equations"

1

Foley, Dawn Christine. "Applications of State space realization of nonlinear input/output difference equations." Thesis, Georgia Institute of Technology, 1999. http://hdl.handle.net/1853/16818.

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2

Li, Bo. "Steady State Solutions for a System of Partial Differential Equations Arising from Crime Modeling." Scholarship @ Claremont, 2016. http://scholarship.claremont.edu/hmc_theses/78.

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I consider a model for the control of criminality in cities. The model was developed during my REU at UCLA. The model is a system of partial differential equations that simulates the behavior of criminals and where they may accumulate, hot spots. I have proved a prior bounds for the partial differential equations in both one-dimensional and higher dimensional case, which proves the attractiveness and density of criminals in the given area will not be unlimitedly high. In addition, I have found some local bifurcation points in the model.
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3

Smario, David J. "Multicorrelation analysis and state space reconstruction /." Online version of thesis, 1994. http://hdl.handle.net/1850/11443.

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4

Ye, Jinglong. "Infinite semipositone systems." Diss., Mississippi State : Mississippi State University, 2009. http://library.msstate.edu/etd/show.asp?etd=etd-07072009-132254.

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5

Zhang, Zhengyang. "A class of state-dependent delay differential equations and applications to forest growth." Thesis, Bordeaux, 2018. http://www.theses.fr/2018BORD0062/document.

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Анотація:
Cette thèse est consacrée à l'étude d'une classe d'équations différentielles à retard dépendant de l'état -- ces équations provenant d'un modèle structuré en taille. La principale motivation de cette thèse provient de la volonté d'ajuster les paramètres du système d'équations étudiées vis-à-vis des données générées par un simulateur de forêts, appelé SORTIE. Deux types de forêts sont étudiés ici: d'une part une forêt ne comportant qu'une seule espèce d'arbre, et d'autre part une forêt comportant deux espèces d'arbres (au chapitre 2). Les simulations numériques du système d'équations correspondent relativement bien aux données générées par SORTIE, ce qui montre que le système considéré peut être utilisé afin d'écrire la dynamique de populations d'une forêt. De plus, un modèle plus étendu prenant en compte la position spatiale des arbres est proposé dans le chapitre 2, dans le cas de forêts possédant deux espèces d'arbres. Les simulations numériques de ce modèle permettent de visualiser la propagation spatiale des forêts. Les chapitres 3 et 4 se concentrent sur l'analyse mathématique des équations différentielles à retard considérées. Les propriétés du semi-flot associé au système sont étudiées au chapitre 3, où l'on démontre en particulier que ce semi-flot n'est pas continu en temps. Le caractère dissipatif et borné du semi-flot, pour des modèles de forêts comportant une ou deux espèces d'arbres, est étudié dans le chapitre 4. En outre, afin d'étudier la dynamique de population d'une forêt (d'une seule espèce d'arbre) après l'introduction d'un parasite, nous construisons dans le chapitre 5 un système proie-prédateur dont la proie (à savoir la forêt) est modélisée par le système d'équations différentielles à retard dépendant de l'état étudié auparavant, et dont le prédateur (à savoir le parasite) est modélisé par une équation différentielle ordinaire. De nombreuses simulations numériques associées à différents scénarios sont faites, afin d'explorer le comportement complexe des solutions du au couplage proie-prédateur et les équations à retard dépendant de l'état
This thesis is devoted to the studies of a class of state-dependent delay differential equations. This class of equations is derived from a size-structured model.The motivation comes from the parameter fittings of this system to a forest simulator called SORTIE. Cases of both single species forest and two-species forest are considered in Chapter 2. The numerical simulations of the system correspond relatively very well to the forest data generated by SORTIE, which shows that this system is able to be used to describe the population dynamics of forests. Moreover, an extended model considering the spatial positions of trees is also proposed in Chapter 2 for the two-species forest case. From the numerical simulations of this spatial model one can see the diffusion of forests in space. Chapter 3 and 4 focus on the mathematical analysis of the state-dependent delay differential equations. The properties of semiflow generated by this system are studied in Chapter 3, where we find that this semiflow is not time-continuous. The boundedness and dissipativity of the semiflow for both single species model and multi-species model are studied in Chapter 4. Furthermore, in order to study the population dynamics after the introduction of parasites into a forest, a predator-prey system consisting of the above state-dependent delay differential equation (describing the forest) and an ordinary differential equation (describing the parasites) is constructed in Chapter 5 (only the single species forest is considered here). Numerical simulations in several scenarios and cases are operated to display the complex behaviours of solutions appearing in this system with the predator-prey relation and the state-dependent delay
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6

Ali, Jaffar. "Multiple positive solutions for classes of elliptic systems with combined nonlinear effects." Diss., Mississippi State : Mississippi State University, 2008. http://library.msstate.edu/etd/show.asp?etd=etd-07082008-153843.

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7

Bramburger, Jason. "Steady State/Hopf Interactions in the Van Der Pol Oscillator with Delayed Feedback." Thèse, Université d'Ottawa / University of Ottawa, 2013. http://hdl.handle.net/10393/24325.

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In this thesis we consider the traditional Van der Pol Oscillator with a forcing dependent on a delay in feedback. The delay is taken to be a nonlinear function of both position and velocity which gives rise to many different types of bifurcations. In particular, we study the Zero-Hopf bifurcation that takes place at certain parameter values using methods of centre manifold reduction of DDEs and normal form theory. We present numerical simulations that have been accurately predicted by the phase portraits in the Zero-Hopf bifurcation to confirm our numerical results and provide a physical understanding of the oscillator with the delay in feedback.
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8

Zeng, Honghai. "A web-based high performance simulation system for transport and retention of dissolved contaminants in soils." Diss., Mississippi State : Mississippi State University, 2002. http://library.msstate.edu/etd/show.asp?etd=etd-10082002-144653.

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9

Nguyen, Hoan Kim Huynh. "Volterra Systems with Realizable Kernels." Diss., Virginia Tech, 2004. http://hdl.handle.net/10919/11153.

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We compare an internal state method and a direct Runge-Kutta method for solving Volterra integro-differential equations and Volterra delay differential equations. The internal state method requires the kernel of the Volterra integral to be realizable as an impulse response function. We discover that when applicable, the internal state method is orders of magnitude more efficient than the direct numerical method. However, constructing state representation for realizable kernels can be challenging at times; therefore, we propose a rational approximation approach to avoid the problem. That is, we approximate the transfer function by a rational function, construct the corresponding linear system, and then approximate the Volterra integro-differential equation. We show that our method is convergent for the case where the kernel is nuclear. We focus our attention on time-invariant realizations but the case where the state representation of the kernel is a time-variant linear system is briefly discussed.
Ph. D.
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10

Trimeloni, Thomas. "Accelerating Finite State Projection through General Purpose Graphics Processing." VCU Scholars Compass, 2011. http://scholarscompass.vcu.edu/etd/175.

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The finite state projection algorithm provides modelers a new way of directly solving the chemical master equation. The algorithm utilizes the matrix exponential function, and so the algorithm’s performance suffers when it is applied to large problems. Other work has been done to reduce the size of the exponentiation through mathematical simplifications, but efficiently exponentiating a large matrix has not been explored. This work explores implementing the finite state projection algorithm on several different high-performance computing platforms as a means of efficiently calculating the matrix exponential function for large systems. This work finds that general purpose graphics processing can accelerate the finite state projection algorithm by several orders of magnitude. Specific biological models and modeling techniques are discussed as a demonstration of the algorithm implemented on a general purpose graphics processor. The results of this work show that general purpose graphics processing will be a key factor in modeling more complex biological systems.
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Книги з теми "Differential system state equations"

1

Yee, H. C. Dynamical approach study of spurious steady-state numerical solutions of nonlinear differential equations. [Washington, D.C: National Aeronautics and Space Administration, 1990.

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2

Yee, H. C. Dynamical approach study of spurious steady-state numerical solutions of nonlinear differential equations. [Washington, D.C: National Aeronautics and Space Administration, 1990.

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3

The Fokker-Planck equation for stochastic dynamical systems and its explicit steady state solutions. Singapore: World Scientific, 1994.

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4

Van, Dao Nguyen, ed. Applied asymptotic methods in nonlinear oscillations. Dordrecht: Kluwer Academic Publishers, 1997.

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5

Glovackaya, Alevtina. Computational model. ru: INFRA-M Academic Publishing LLC., 2020. http://dx.doi.org/10.12737/1013723.

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The textbook covers the basics of classical numerical methods of computational mathematics used for solving linear and nonlinear equations and systems; interpolation and approximation of functions; numerical integration and differentiation; solutions of ordinary differential equations by methods of one-dimensional and multidimensional optimization. Meets the requirements of the Federal state educational standards of higher education of the latest generation. It is intended for students of higher educational institutions studying in the discipline "Numerical methods".
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6

Seslavin, Andrey. Theory of automatic control. Linear, continuous systems. ru: INFRA-M Academic Publishing LLC., 2021. http://dx.doi.org/10.12737/1014654.

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The textbook presents the basics of the classical theory of automatic control, based on mathematical models of real systems, given in the form of systems of linear differential equations with constant coefficients. Methods based on Laplace and Fourier transforms, stability, controllability, and observability theory, as well as directed graph theory and linear algebra are used. Meets the requirements of the federal state educational standards of higher education of the latest generation. For students of higher educational institutions studying in the areas of training and specialties 15.00.00 "Mechanical Engineering", 27.00.00 "Management in technical systems".
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7

Arendt, Wolfgang, Joseph A. Ball, Jussi Behrndt, Karl-Heinz Förster, Volker Mehrmann, and Carsten Trunk, eds. Spectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations. Basel: Springer Basel, 2012. http://dx.doi.org/10.1007/978-3-0348-0297-0.

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8

Maury, Bertrand. The Respiratory System in Equations. Milano: Springer Milan, 2013.

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9

Ilchmann, Achim. Surveys in Differential-Algebraic Equations I. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013.

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10

Differential equations and dynamical systems. 2nd ed. New York: Springer, 1996.

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Частини книг з теми "Differential system state equations"

1

Kim, A. V. "Systems with State Delays." In Functional Differential Equations, 131–45. Dordrecht: Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-017-1630-7_10.

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2

Hofer, Eberhard P., Bernd Tibken, and Frank Lehn. "Differential Equations with State-Dependent Delays." In Online Optimization of Large Scale Systems, 413–32. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-662-04331-8_22.

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3

Kolmanovskii, V., and A. Myshkis. "State estimates of stochastic systems with delay." In Applied Theory of Functional Differential Equations, 183–98. Dordrecht: Springer Netherlands, 1992. http://dx.doi.org/10.1007/978-94-015-8084-7_8.

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4

Ghergu, Marius. "Steady-state Solutions for a General Brusselator System." In Modern Aspects of the Theory of Partial Differential Equations, 153–66. Basel: Springer Basel, 2011. http://dx.doi.org/10.1007/978-3-0348-0069-3_9.

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5

Delchamps, David F. "Linear Differential Equations: Existence and Uniqueness Theorems." In State Space and Input-Output Linear Systems, 31–49. New York, NY: Springer New York, 1998. http://dx.doi.org/10.1007/978-1-4612-3816-4_3.

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6

Kolmanovskii, V., and A. Myshkis. "State Estimates of Systems with Delay." In Introduction to the Theory and Applications of Functional Differential Equations, 573–99. Dordrecht: Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-017-1965-0_16.

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7

Wu, Jianhong. "Generators and Decomposition of State Spaces for Linear Systems." In Theory and Applications of Partial Functional Differential Equations, 65–110. New York, NY: Springer New York, 1996. http://dx.doi.org/10.1007/978-1-4612-4050-1_4.

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8

Bonnans, Frédéric, and Eduardo Casas. "A boundary Pontryagin’s principle for the optimal control of state-constrained elliptic systems." In Optimization, Optimal Control and Partial Differential Equations ISNM 107, 241–49. Basel: Birkhäuser Basel, 1992. http://dx.doi.org/10.1007/978-3-0348-8625-3_22.

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9

Crouch, P. E., and F. Lamnabhi-Lagarrigue. "State space realizations of nonlinear systems defined by input-output differential equations." In Analysis and Optimization of Systems, 138–49. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/bfb0042209.

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10

Erman, Sertaç. "Stability Analysis of Some Dynamic Economic Systems Modeled by State-Dependent Delay Differential Equations." In Contributions to Economics, 227–40. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-78494-6_11.

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Тези доповідей конференцій з теми "Differential system state equations"

1

PEETERS, R. L. M., and B. HANZON. "IDENTIFIABILITY OF HOMOGENEOUS POLYNOMIAL SYSTEMS USING THE STATE ISOMORPHISM APPROACH." In Proceedings of the International Conference on Differential Equations. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812702067_0097.

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2

Drǎgan, Vasile F., and Achim Ioniţǎ. "Exponential stability for singularly perturbed systems with state delays." In The 6'th Colloquium on the Qualitative Theory of Differential Equations. Szeged: Bolyai Institute, SZTE, 1999. http://dx.doi.org/10.14232/ejqtde.1999.5.6.

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3

Gusev, Mikhail. "On reachability analysis for nonlinear control systems with state constraints." In The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications (Madrid, Spain). American Institute of Mathematical Sciences, 2015. http://dx.doi.org/10.3934/proc.2015.0579.

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4

Insperger, Ta´mas, Ga´bor Ste´pa´n, Ferenc Hartung, and Janos Turi. "State Dependent Regenerative Delay in Milling Processes." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-85282.

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Traditional models of regenerative machine tool chatter use constant time delays assuming that the period between two subsequent cuts is a constant determined definitely by the spindle speed. These models result in delay-differential equations with constant time delay. If the vibrations of the tool relative to the workpiece are also included in the surface regeneration model, then the resulted time delay is not constant, but it depends on the actual and a delayed position of the tool. In this case, the governing equation is a delay-differential equation with state dependent time delay. Equations with state dependent delays can not be linearized in the traditional sense, but there exists linear equations that can be associated to them. This way, the local behavior of the system with state dependent delays can be investigated. In this study, a two degree of freedom model is presented for milling process. A thorough modeling of the regeneration effect results in the governing delay-differential equation with state dependent time delay. It is shown through the linearization of the nonlinear equation that an additional term arises in the linearized equation of motion due to the state-dependency of the time delay.
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Trigeassou, J. C., and N. Maamri. "State space modeling of fractional differential equations and the initial condition problem." In 2009 6th International Multi-Conference on Systems, Signals and Devices (SSD). IEEE, 2009. http://dx.doi.org/10.1109/ssd.2009.4956721.

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6

Negrut, Dan, and Edward J. Haug. "State-Space Based Implicit Integration of the Differential-Algebraic Equations of Multibody Dynamics." In ASME 1999 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/detc99/vib-8240.

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Abstract Three methods for the state-space based implicit integration of differential-algebraic equations of multibody dynamics are summarized and numerically compared. In the state-space approach, the time evolution of a mechanical system is characterized using a number of generalized coordinates equal with the number of degrees of freedom of the system. In this paper these independent generalized coordinates are a subset of the Cartesian position coordinates and orientation Euler parameters of body centroidal reference frames. Depending on the method, the independent generalized coordinates are implicitly integrated and dependent quantities (including Lagrange multipliers) are determined to satisfy constraint equations at position, velocity, and acceleration levels. Five computational algorithms based on the proposed methods are used to simulate the motion of a stiff 14-body vehicle model. Results show that the proposed methods deal effectively with challenges posed by stiff mechanical system simulation. A comparison with a state-space based explicit algorithm for the simulation of the same model indicates a speed-up of approximately two orders of magnitude.
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7

Verdugo, Anael, and Richard H. Rand. "Delay Differential Equations in the Dynamics of Gene Copying." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-34214.

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We analyze a model of gene transcription and protein synthesis which has been previously presented in the biological literature. The model takes the form of an ODE (ordinary differential equation) coupled to a DDE (delay differential equation), the state variables being concentrations of messenger RNA and protein. The delay is assumed to depend on the concentration of mRNA and is therefore state-dependent. Linear analysis gives a critical time delay beyond which a periodic motion is born in a Hopf bifurcation. Lindstedt’s method is applied to the nonlinear system, resulting in closed form approximate expressions for the amplitude and frequency of oscillation.
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8

Khasawneh, Firas A., Brian P. Mann, and Bhavin Patel. "A State-Space Temporal Finite Element Approach for Stability Investigations of Delay Equations." In ASME 2009 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. ASMEDC, 2009. http://dx.doi.org/10.1115/smasis2009-1263.

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This paper describes a new approach to examine the stability of delay differential equations that builds upon prior work using temporal finite element analysis. In contrast to previous analyses, which could only be applied to second order delay differential equations, the present manuscript develops an approach which can be applied to a broader class of systems — systems that may be written in the form of a state space model. A primary outcome from this work is a generalized framework to investigate the asymptotic stability of autonomous delay differential equations with a single time delay. Furthermore, this approach is shown to be applicable to time-periodic delay differential equations and equations that are piecewise continuous.
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9

Gururaja Rao, Lakshmi, and James T. Allison. "Generalized Viscoelastic Material Design With Integro-Differential Equations and Direct Optimal Control." In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/detc2015-46768.

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Rheological material properties are examples of function-valued quantities that depend on frequency (linear viscoelasticity), input amplitude (nonlinear material behavior), or both. This dependence complicates the process of utilizing these systems in engineering design. In this article, we present a methodology to model and optimize design targets for such rheological material functions. We show that for linear viscoelastic systems simple engineering design assumptions can be relaxed from a conventional spring-dashpot model to a more general linear viscoelastic relaxation kernel, K(t). While this approach expands the design space and connects system-level performance with optimal material design functions, it entails significant numerical difficulties. Namely, the associated governing equations involve a convolution integral, thus forming a system of integro-differential equations. This complication has two important consequences: 1) the equations representing the dynamic system cannot be written in a standard state space form as the time derivative function depends on the entire past state history, and 2) the dependence on prior time-history increases time derivative function computational expense. Previous studies simplified this process by incorporating parameterizations of K(t) using viscoelastic models such as Maxwell or critical gel models. While these simplifications support efficient solution, they limit the type of viscoelastic materials that can be designed. This article introduces a more general approach that can explore arbitrary K(t) designs using direct optimal control methods. In this study, we analyze a nested direct optimal control approach to optimize linear viscoelastic systems with no restrictions on K(t). The study provides new insights into efficient optimization of systems modeled using integro-differential equations. The case study is based on a passive vibration isolator design problem. The resulting optimal K(t) functions can be viewed as early-stage design targets that are material agnostic and allow for creative material design solutions. These targets may be used for either material-specific selection or as targets for later-stage design of novel materials.
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Marvel, Skylar W., and Cranos M. Williams. "Set membership state and parameter estimation for nonlinear differential equations with sparse discrete measurements." In 2012 IEEE International Conference on Systems, Man and Cybernetics - SMC. IEEE, 2012. http://dx.doi.org/10.1109/icsmc.2012.6377679.

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Звіти організацій з теми "Differential system state equations"

1

Caraus, Lurie, and Zhilin Li. A Direct Method and Convergence Analysis for Some System of Singular Integro-Differential Equations. Fort Belvoir, VA: Defense Technical Information Center, January 2003. http://dx.doi.org/10.21236/ada451436.

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2

Jung, Paul H., Jean-Claude Thill, and Luis Armando Galvis-Aponte. State Failure, Violence, and Trade: Dangerous Trade Routes in Colombia. Banco de la República, December 2021. http://dx.doi.org/10.32468/dtseru.303.

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We investigate the effect of domestic armed violence brought about by political instability on the geography of distance frictions in freight mobility and the resulting differential access of regions to global markets. The Colombian transportation system has been found to be impeded by deficiencies in landside transport infrastructure and institutions, and by fragmented political environments. The micro-level analysis of U.S.-bounded export shipping records corroborates that export freight shipping from inland regions is re-routed to avoid exposures to domestic armed violence despite greatly extended landside and maritime shipping distances. We exploit the trajectories of freight shipping from Colombian regions and spatial patterns of violent armed conflicts to see how unstable geopolitical environments are detrimental to freight shipping mobility and market openness. The discrete choice model shows that the shipping flow is greatly curbed by the extended re-routing due to domestic armed violence and that inland regions have restricted access to the global market. The perception of risk and re-routing behavior is found heterogeneous across shipments and conditional to shipment characteristics, such as commodity type, freight value and shipper sizes. The results highlight that political stability must be accommodated for improved freight mobility and export-oriented economic development in the global South.
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3

Lehe, Lewis, Sairpaneeth Devunuri, Javier Rondan, and Ayush Pandey. Taxation of Ride-hailing. Illinois Center for Transportation, December 2021. http://dx.doi.org/10.36501/0197-9191/21-040.

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This report is a guide to the practice of taxing ride-hailing at the state and local levels in the United States. The information is based on a survey of legislation, news articles, journal articles, revenue data, and interviews. We first review the literature and provide a history of ride-hailing and the practice of ride-hailing. We then profile all ride-hailing taxes in the United States, classifying these taxes according to common attributes and pointing out what details of legislation or history distinguishes each tax. One important distinction is between ad valorem taxes, levied as a percentage of fare or revenues, and “per-ride” taxes levied as a flat charge per ride. Another distinction is the differential treatment of shared and single rides. We provide extensive references to laws and ordinances as well as propose a system to classify the state legal environments under which ride-hailing is taxed. States fall into five regimes: (1) a “hands-off” regime wherein local governments are permitted wide leeway; (2) a “tax-free” regime wherein local taxes are prohibited and the state does not impose a tax; (3) a “state-tax-only” regime wherein local taxes are prohibited but the state levies taxes for its own use; (4) a “revenue-sharing” regime wherein the state levies taxes and distributes them to local governments; and (5) a “local-option” regime wherein local governments can opt into participating in a tax system regulated by the state. We make nine recommendations for Illinois policymakers considering taxes on ride-hailing, with the most important being that the state pass legislation clarifying and regulating the rights of local governments to levy such taxes.
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Prusky, Dov, Nancy P. Keller, and Amir Sherman. global regulation of mycotoxin accumulation during pathogenicity of Penicillium expansum in postharvest fruits. United States Department of Agriculture, January 2014. http://dx.doi.org/10.32747/2014.7600012.bard.

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Background to the topic- Penicilliumas a postharvest pathogen and producer of the mycotoxin PAT. Penicilliumspp. are destructive phytopathogens, capable of causing decay in many deciduous fruits, during postharvest handling and storage; and the resulting losses can amount to 10% of the stored produce and the accumulation of large amounts of the mycotoxinpatulin. The overall goal of this proposal is to identify critical host and pathogen factors that modulate P. expansummycotoxin genes and pathways which are required for PAT production and virulence. Our preliminary results indicated that gluconic acid are strongly affecting patulin accumulation during colonization. P. expansumacidifies apple fruit tissue during colonization in part through secretion of gluconic acid (GLA). Several publications suggested that GLA accumulation is an essential factor in P. expansumpathogenicity. Furthermore, down regulation of GOX2 significantly reduced PAT accumulation and pathogenicity. PAT is a polyketide and its biosynthesis pathway includes a 15-gene cluster. LaeA is a global regulator of mycotoxin synthesis. It is now known that patulin synthesis might be subjected to LaeA and sometimes by environmental sensing global regulatory factors including the carbon catabolite repressor CreA as well as the pH regulator factor PacC and nitrogen regulator AreA. The mechanisms by which LaeA regulates patulin synthesis was not fully known and was part of our work. Furthermore, the regulatory system that controls gene expression in accordance with ambient pH was also included in our work. PacC protein is in an inactive conformation and is unable to bind to the promoter sites of the target genes; however, under alkaline growth conditions activated PacC acts as both an activator of alkaline-expressed genes and a repressor of acid-expressed genes. The aims of the project- This project aims to provide new insights on the roles of LaeA and PacC and their signaling pathways that lead to GLA and PAT biosynthesis and pathogenicity on the host. Specifically, our specific aims were: i) To elucidate the mechanism of pH-controlled regulation of GLA and PAT, and their contribution to pathogenesis of P. expansum. We are interested to understanding how pH and/or GLA impact/s under PacC regulation affect PAT production and pathogenesis. ii) To characterize the role of LaeA, the global regulator of mycotoxin production, and its effect on PAT and PacC activity. iii) To identify the signaling pathways leading to GLA and PAT synthesis. Using state- of-the-art RNAseq technologies, we will interrogate the transcriptomes of laeAand pacCmutants, to identify the common signaling pathways regulating synthesis of both GLA and PAT. Major conclusions, solutions, achievements- In our first Aim our results demonstrated that ammonia secreted at the leading edge of the fungal colony induced transcript activation of the global pH modulator PacC and PAT accumulation in the presence of GLA. We assessed these parameters by: (i) direct exogenous treatment of P. expansumgrowing on solid medium; (ii) direct exogenous treatment on colonized apple tissue; (iii) growth under self-ammonia production conditions with limited carbon; and (iv) analysis of the transcriptional response to ammonia of the PAT biosynthesis cluster. Ammonia induced PAT accumulation concurrently with the transcript activation of pacCand PAT biosynthesis cluster genes, indicating the regulatory effect of ammonia on pacCtranscript expression under acidic conditions. Transcriptomic analysis of pH regulated processes showed that important genes and BARD Report - Project 4773 Page 2 of 10 functionalities of P. expansumwere controlled by environmental pH. The differential expression patterns of genes belonging to the same gene family suggest that genes were selectively activated according to their optimal environmental conditions to enable the fungus to cope with varying conditions and to make optimal use of available enzymes. Concerning the second and third Aims, we demonstrated that LaeA regulates several secondary metabolite genes, including the PAT gene cluster and concomitant PAT synthesis invitro. Virulence studies of ΔlaeAmutants of two geographically distant P. expansumisolates (Pe-21 from Israel and Pe-T01 from China) showed differential reduction in disease severity in freshly harvested fruit ranging from no reduction for Ch-Pe-T01 strains in immature fruit to 15–25% reduction for both strains in mature fruit, with the ΔlaeAstrains of Is-Pe-21 always showing a greater loss in virulence. Results suggest the importance of LaeA regulation of PAT and other secondary metabolites on pathogenicity. Our work also characterized for the first time the role of sucrose, a key nutritional factor present in apple fruit, as a negative regulator of laeAexpression and consequent PAT production in vitro. This is the first report of sugar regulation of laeAexpression, suggesting that its expression may be subject to catabolite repression by CreA. Some, but not all of the 54 secondary metabolite backbone genes in the P. expansumgenome, including the PAT polyketide backbone gene, were found to be regulated by LaeA. Together, these findings enable for the first time a straight analysis of a host factor that potentially activates laeAand subsequent PAT synthesis.
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District level baseline survey of family planning program in Uttar Pradesh: Ghaziabad. Population Council, 1995. http://dx.doi.org/10.31899/rh1995.1003.

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Uttar Pradesh is the most populous state in India with 139 million individuals, per the 1991 census. The Sample Registration System in 1992 indicated a high population growth rate of 2.3 percent and a very high birth rate of 36.2 per 1,000. Several measures have been taken to contain the growth and bring a rapid decline in the fertility rate. The Government of India and USAID began the Innovations in Family Planning Services Project under the management of the State Innovations in Family Planning Services Agency. The goal was to reduce the fertility rate in Uttar Pradesh by expanding and improving family planning (FP) services. Since there has been differential impact of FP services over the years in the state’s different districts, it was considered desirable to take up the district as a unit and develop an adequate data base for generating suitable intervention programs. Baseline surveys were conducted in 14 districts in different regions of the state. The Centre for Development Research and Training, Madras, conducted the surveys in Ghaziabad and Tehri Garhwal. This preliminary report contains the details of the survey conducted in Ghaziabad district.
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