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Weak random periodic solutions of random dynamical systems
Canadian Mathematical Bulletin, 2023 AbstractWe first introduce the concept of weak random periodic solutions of random dynamical systems. Then, we discuss the existence of such periodic solutions. Further, we introduce the definition of weak random periodic measures and study their relationship with weak random periodic solutions.
Sun, Wei, Zheng, Zuo-Huan
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Theory of the Loschmidt echo and dynamical quantum phase transitions in disordered Fermi systems
Physical Review Research, 2023 In this work we develop the theory of the Loschmidt echo and dynamical phase transitions in noninteracting strongly disordered Fermi systems after a quench.
Tuomas I. Vanhala, Teemu Ojanen
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On the Criticality of Adaptive Boolean Network Robots
Entropy, 2022 Systems poised at a dynamical critical regime, between order and disorder, have been shown capable of exhibiting complex dynamics that balance robustness to external perturbations and rich repertoires of responses to inputs.
Michele Braccini +3 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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Distributional chaos in random dynamical systems [PDF]
Journal of Difference Equations and Applications, 2019 In this paper, we introduce the notion of distributional chaos and the measure of chaos for random dynamical systems generated by two interval maps. We give some sufficient conditions for a zero measure of chaos and examples of chaotic systems. We demonstrate that the chaoticity of the functions that generate a system does not, in general, affect the ...
Jozef Kováč, Katarína Janková
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Conditional random matrix ensembles and the stability of dynamical systems
New Journal of Physics, 2015 Random matrix theory (RMT) has found applications throughout physics and applied mathematics, in subject areas as diverse as communications networks, population dynamics, neuroscience, and models of the banking system.
Paul Kirk +3 more
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Quantum State Tomography in Nonequilibrium Environments
Photonics, 2023 We generalize an approach to studying the quantum state tomography (QST) of open systems in terms of the dynamical map in Kraus representation within the framework of dynamic generation of informationally complete positive operator-valued measures.
Haonan Chen +6 more
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Upper semicontinuity of random attractors for non-compact random dynamical systems
Electronic Journal of Differential Equations, 2009 The upper semicontinuity of random attractors for non-compact random dynamical systems is proved when the union of all perturbed random attractors is precompact with probability one.
Bixiang Wang
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Center manifolds for random dynamical systems with generalized trichotomies
Electronic Journal of Qualitative Theory of Differential EquationsIn this paper, we consider small perturbations of linear Random Dynamical Systems evolving on a Banach space and admitting a general form of trichotomy.
António Bento, Helder Vilarinho
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Learning dynamical systems with hit-and-run random feature maps
Nature CommunicationsWe show how random feature maps can be used to forecast dynamical systems with excellent forecasting skill. We consider the tanh activation function and judiciously choose the internal weights in a data-driven manner such that the resulting features ...
Pinak Mandal, Georg A. Gottwald
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