Results 1 to 10 of about 5,959 (167)
Topological stability and shadowing of zero-dimensional dynamical systems
Discrete and Continuous Dynamical Systems, 2019 In this paper, we examine the notion of topological stability and its relation to the shadowing properties in zero-dimensional spaces. Several counter-examples on the topological stability and the shadowing properties are given.
Noriaki Kawaguchi
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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.
Christian B Mendl, Jan Carl Budich
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Experimental quantum simulation of non-Hermitian dynamical topological states using stochastic Schrödinger equation [PDF]
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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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
Jian-Dong Yin, M. Dong
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Topological stability criteria for networking dynamical systems with Hermitian Jacobian
European Journal of Applied Mathematics, 2016 The central theme of complex systems research is to understand the emergent macroscopic properties of a system from the interplay of its microscopic constituents. The emergence of macroscopic properties is often intimately related to the structure of the microscopic interactions. Here, we present an analytical approach for deriving necessary conditions
Anne-Ly Do +4 more
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Topological conjugacy and structural stability for discrete dynamical systems [PDF]
Bulletin of the American Mathematical Society, 1972 Topological conjugacy and various concepts of structural stability are defined, motivated, and criticized. Two basic problems emerge: characterization of structural stability and classification up to topological conjugacy. Solutions to these problems are
J. Robbin
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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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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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SARAJEVO JOURNAL OF MATHEMATICS, 2012 We prove that the level curves of some differentiable functions of two variables with unique critical point are diffeomorphic to the circle T, and show how this result can be used in the study of local stability of dynamical systems in dimension 2 with ...
G. Bastien, M. Rogalski
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