Results 21 to 30 of about 5,568 (185)
Shadowing property for nonautonomous dynamical systems
Contemporary Mathematics. Fundamental Directions, 2023 A new approach based on the analysis of the influence of a single perturbation is proposed as a test for the shadowing property for a broad class of dynamical systems (in particular, non-autonomous) under a variety of perturbations. Applications for several interesting cases are considered in detail.
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Pullback Attractors for Nonclassical Diffusion Equations in Noncylindrical Domains
International Journal of Mathematics and Mathematical Sciences, 2012 The existence and uniqueness of a variational solution are proved for the following nonautonomous nonclassical diffusion equation ๐ข๐กโ๐ฮ๐ข๐กโฮ๐ข+๐(๐ข)=๐(๐ฅ,๐ก),๐โ(0,1], in a noncylindrical domain with homogeneous Dirichlet boundary conditions, under the ...
Cung The Anh, Nguyen Duong Toan
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Lagrangian Descriptors for Stochastic Differential Equations: A Tool for Revealing the Phase Portrait of Stochastic Dynamical Systems [PDF]
, 2016 In this paper we introduce a new technique for depicting the phase portrait of stochastic differential equations. Following previous work for deterministic systems, we represent the phase space by means of a generalization of the method of Lagrangian ...
Balibrea-Iniesta, Francisco +3 more
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Controllability and Observability of Nonautonomous Riesz-Spectral Systems
Abstract and Applied Analysis, 2018 There are many industrial and biological reaction diffusion systems which involve the time-varying features where certain parameters of the system change during the process.
Sutrima Sutrima +2 more
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Entropy, 2018 In the paper, we consider local aspects of the entropy of nonautonomous dynamical systems. For this purpose, we introduce the notion of a (asymptotical) focal entropy point.
Ewa Korczak-Kubiak +2 more
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An invariant set bifurcation theory for nonautonomous nonlinear evolution equations
Electronic Journal of Qualitative Theory of Differential Equations, 2020 In this paper we establish an invariant set bifurcation theory for the nonautonomous dynamical system $(\varphi_\lambda,\theta)_{X,\mathcal H}$ generated by the evolution equation \begin{equation}\label{e0}u_t+Au=\lambda u+p(t,u),\hspace{0.4cm} p\in ...
Xuewei Ju, Ailing Qi
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Transport in Transitory Dynamical Systems [PDF]
, 2010 We introduce the concept of a "transitory" dynamical system---one whose time-dependence is confined to a compact interval---and show how to quantify transport between two-dimensional Lagrangian coherent structures for the Hamiltonian case.
B. A. Mosovsky, J. D. Meiss, Kaper T. J.
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Nonautonomous Discrete Neuron Model with Multiple Periodic and Eventually Periodic Solutions
Discrete Dynamics in Nature and Society, 2015 We introduce a nonautonomous discrete neuron model based on the Rulkov map and investigate its dynamics. Using both the linear stability and bifurcation analyses of the system of piecewise difference equations, we determine dynamical bifurcations and ...
Alexander N. Pisarchik +2 more
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The mean-square dichotomy spectrum and a bifurcation to a mean-square attractor [PDF]
, 2014 The dichotomy spectrum is introduced for linear mean-square random dynamical systems, and it is shown that for finite-dimensional mean-field stochastic differential equations, the dichotomy spectrum consists of finitely many compact intervals. It is then
Doan, Thai Son +2 more
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Pullback incremental attraction
Nonautonomous Dynamical Systems, 2014 A pullback incremental attraction, a nonautonomous version of incremental stability, is introduced for nonautonomous systems that may have unbounded limiting solutions.
Kloeden Peter E., Lorenz Thomas
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