Representation of exact trajectory solutions for chaotic one-dimensional maps in Schroder form [PDF]
Известия высших учебных заведений: Прикладная нелинейная динамика, 2023 Purpose of the article is to illustrate the genesis, meaning and significance of the functional Schroder equation, introduced in the theory of iterations of rational functions, for the theory of deterministic chaos by analytical calculations of ...
Anikin, Valerij Mihajlovich
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Stochastic stability of viscoelastic systems under Gaussian and Poisson white noise excitations [PDF]
, 2018 As the use of viscoelastic materials becomes increasingly popular, stability of viscoelastic structures under random loads becomes increasingly important.
Gu, J, Li, X, Ma, F, Xu, W
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Numerical Methods That Preserve a Lyapunov Function for Ordinary Differential Equations
Mathematics, 2022 The paper studies numerical methods that preserve a Lyapunov function of a dynamical system, i.e., numerical approximations whose energy decreases, just like in the original differential equation.
Yadira Hernández-Solano, Miguel Atencia
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Lyapunov Functionals in Integral Equations
Axioms, 2023 Lyapunov functions/functionals have found their footing in Volterra integro-differential equations. This is not the case for integral equations, and it is therefore further explored in this paper. In this manuscript, we utilize Lyapunov functionals combined with Laplace transform to qualitatively analyze the solutions of the integral equation In ...
Youssef N. Raffoul, Joseph Raffoul
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Lyapunov Stability of the Generalized Stochastic Pantograph Equation
Journal of Mathematics, 2018 The purpose of the paper is to study stability properties of the generalized stochastic pantograph equation, the main feature of which is the presence of unbounded delay functions. This makes the stability analysis rather different from the classical one.
Ramazan Kadiev, Arcady Ponosov
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Lyapunov functions for linear nonautonomous dynamical equations on time scales [PDF]
, 2006 The existence of a Lyapunov function is established following a method of Yoshizawa for the uniform exponential asymptotic stability of the zero solution of a nonautonomous linear dynamical equation on a time scale with uniformly bounded ...
Kloeden, Peter E., Zmorzynska, Alexandra
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Matrix iteration algorithms for solving the generalized Lyapunov matrix equation
Advances in Difference Equations, 2021 In this paper, we first recall some well-known results on the solvability of the generalized Lyapunov equation and rewrite this equation into the generalized Stein equation by using Cayley transformation.
Juan Zhang, Huihui Kang, Shifeng Li
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A Perron type theorem for positive solutions of functional differential equations
Electronic Journal of Qualitative Theory of Differential Equations, 2018 A nonlinear perturbation of a linear autonomous retarded functional differential equation is considered. According to a Perron type theorem, with the possible exception of small solutions the Lyapunov exponents of the solutions of the perturbed equation ...
Mihály Pituk
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Applied Lyapunov Stability for Some Nonlinear Stochastic Differential Equations
Tikrit Journal of Pure Science, 2023 In this paper, we applied and explain the stability to some linear and non-linear stochastic differential equations by using the Lyapunov direct second method, after finding the stochastic differential equation which obtained by applying the (Ito ...
Nibal Sabah Abdurahman +1 more
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Chaotic Properties of Dilute Two and Three Dimensional Random Lorentz Gases I: Equilibrium Systems
, 1997 We compute the Lyapunov spectrum and the Kolmogorov-Sinai entropy for a moving particle placed in a dilute, random array of hard disk or hard sphere scatterers - i.e. the dilute Lorentz gas model.
A. Crisanti +47 more
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