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Fixed-point topology meets fractal memory: a Kutumba-stabilized framework for nonlocal fractal–fractional dynamics [PDF]
Scientific ReportsThis paper presents an innovative synthesis of generalised fixed-point theory, advanced topological degree methodologies, and high-order computational frameworks for memory-driven dynamical systems. We expand contraction principles in complete metric and
R. Aruna Devi +6 more
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Stability of dynamical quantum phase transitions in quenched topological insulators: From multiband to disordered systems [PDF]
Physical Review B, 2019 Dynamical quantum phase transitions (DQPTs) represent a counterpart in non-equilibrium quantum time evolution of thermal phase transitions at equilibrium, where real time becomes analogous to a control parameter such as temperature. In quenched quantum systems, recently the occurrence of DQPTs has been demonstrated, both with theory and experiment, to ...
Christian B Mendl, Jan Carl Budich
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Topological dynamics of control systems: Stability and attraction
Nonlinear Analysis: Theory, Methods & Applications, 1986 The authors study topological properties of control systems considered as dynamical polysystems. In this context they introduce such notions as stability, attraction, limit set and various prolongational sets. They derive some basic properties of these sets related to the stability question.
Andrea Bacciotti
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Topological stability and shadowing of zero-dimensional dynamical systems
Discrete and Continuous Dynamical Systems, 2019 The topological stability introduced by \textit{P. Walters} [Lect. Notes Math. 668, 231-244 (1978; Zbl 0403.58019)] is a kind of structural stability defined for all homeomorphisms of compact metric spaces. Under this assumption, \textit{P. Walters} proved that topologically stable homeomorphisms satisfy the shadowing property.
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The modal sensitivity, robustness and roughness of dynamic systems (review article) [PDF]
Научно-технический вестник информационных технологий, механики и оптики, 2021 The review focuses on the development of theories of sensitivity and modal sensitivity, robustness and roughness of dynamic systems. In modern theory of dynamic systems and automatic control systems, there is a need to study the properties of sensitivity,
Roman O. Omorov
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Topological Conditions for In-Network Stabilization of Dynamical Systems [PDF]
IEEE Journal on Selected Areas in Communications, 2013 We study the problem of stabilizing a linear system over a wireless network using a simple in-network computation method. Specifically, we study an architecture called the "Wireless Control Network" (WCN), where each wireless node maintains a state, and periodically updates it as a linear combination of neighboring plant outputs and node states.
Miroslav Pajic +3 more
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npj Quantum Information, 2022 Noise is ubiquitous in real quantum systems, leading to non-Hermitian quantum dynamics, and may affect the fundamental states of matter. Here we report in an experiment a quantum simulation of the two-dimensional non-Hermitian quantum anomalous Hall (QAH)
Zidong Lin +10 more
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Noise-to-State Stability in Probability for Random Complex Dynamical Systems on Networks
Mathematics, 2022 This paper studies noise-to-state stability in probability (NSSP) for random complex dynamical systems on networks (RCDSN). On the basis of Kirchhoff’s matrix theorem in graph theory, an appropriate Lyapunov function which combines with every subsystem ...
Cheng Peng +3 more
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Localized dissipative vortices in chiral nematic liquid crystal cells
Physical Review Research, 2022 Solitary waves and solitons have played a fundamental role in understanding nonlinear phenomena and emergent particle-type behaviors in out-of-equilibrium systems.
M. G. Clerc +2 more
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Topological stability and shadowing of dynamical systems from measure theoretical viewpoint
Topological Methods in Nonlinear Analysis, 2021 In this paper it is proved that a topologically stable invariant measure has no sinks or sources in its support; an expansive homeomorphism is topologically stable if it exhibits a topologically stable nonatomic Borel support measure and a continuous map has the shadowing property if there exists an invariant measure with the shadowing property such ...
Jiandong Yin, Meihua Dong
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