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Random periodic solutions of random dynamical systems
Journal of Differential Equations, 2009 In this paper, we give the definition of the random periodic solutions of random dynamical systems. We prove the existence of such periodic solutions for a $C^1$ perfect cocycle on a cylinder using a random invariant set, the Lyapunov exponents and the pullback of the cocycle.
Huaizhong Zhao
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Stochastic Safety for Random Dynamical Systems [PDF]
2021 American Control Conference (ACC), 2021 In the paper, we study the so-called p-safety of a random dynamical system. We generalize the existing results for safety barrier certificates for deterministic dynamical systems and Markov processes. Moreover, we consider the case of random obstacles, modelled as random sets.
Bujorianu, Manuela L. +2 more
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Invariant measures and random attractors of stochastic delay differential equations in Hilbert space
Electronic Journal of Qualitative Theory of Differential Equations, 2022 This paper is devoted to a general stochastic delay differential equation with infinite-dimensional diffusions in a Hilbert space. We not only investigate the existence of invariant measures with either Wiener process or Lévy jump process, but also ...
Shangzhi Li, Shangjiang Guo
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Random Conformal Dynamical Systems [PDF]
Geometric and Functional Analysis, 2007 We consider random dynamical systems such as groups of conformal transformations with a probability measure, or transversaly conformal foliations with a Laplace operator along the leaves, in which case we consider the holonomy pseudo-group. We prove that either there exists a measure invariant under all the elements of the group (or the pseudo-group ...
Deroin, Bertrand, Kleptsyn, Victor A.
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On the Concept of Complexity of Random Dynamical Systems [PDF]
International Journal of Modern Physics B, 1998 We show how to introduce a characterization the "complexity" of random dynamical systems. More precisely we propose a suitable indicator of complexity in terms of the average number of bits per time unit necessary to specify the sequence generated by these systems.
LORETO, Vittorio +2 more
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Unification of random dynamical decoupling and the quantum Zeno effect
New Journal of Physics, 2022 Periodic deterministic bang–bang dynamical decoupling and the quantum Zeno effect are known to emerge from the same physical mechanism. Both concepts are based on cycles of strong and frequent kicks provoking a subdivision of the Hilbert space into ...
Alexander Hahn +2 more
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PROGRAM GENERATOR PROCESSES INDUCED BY NONLINEAR DYNAMIC SYSTEM WITH IMPULS NOISES [PDF]
Vestnik KRAUNC: Fiziko-Matematičeskie Nauki, 2017 The article considers nonlinear dynamic systems with impulse perturbation. The described method of generation of impulse random processes on a computer. On the example of the Lorenz system are considered a software module.
Kazakov E. A.
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Mathematics, 2023 An optimal control for a dynamical system optimizes a certain objective function. Here, we consider the construction of an optimal control for a stochastic dynamical system with a random structure, Poisson perturbations and random jumps, which makes the ...
Taras Lukashiv +4 more
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Anomalous correlation-induced dynamical phase transitions
Scientific Reports, 2023 The nonanalyticity of the Loschmidt echo at critical times in quantum quenched systems is termed as the dynamical quantum phase transition, extending the notion of quantum criticality to a nonequilibrium scenario.
Niaz Ali Khan +3 more
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RANDOM DYNAMICAL SYSTEMS IN ECONOMICS [PDF]
Stochastics and Dynamics, 2001 This paper surveys recent advances in the application of random dynamical systems theory in economics. It illustrates the usefulness of this framework for modeling and analysis of economic phenomena with stochastic components, mainly focusing on stochastic dynamic models of economic growth.
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