Results 271 to 280 of about 6,906 (308)

Nontrivial Global Attractors in 2-D Multistable Attractor Neural Networks

IEEE Transactions on Neural Networks, 2009
Attractor dynamics is a crucial problem for attractor neural networks, as it is the underling computational mechanism for memory storage and retrieval in neural systems. This brief studies a class of attractor network consisting of linearized threshold neurons, and analyzes global attractors based on a parameterized 2-D model.
Lan Zou, Huajin Tang, Kay Chen Tan, Weinian Zhang   +3 more
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Global Attractors and Robustness of the Boissonade System

Journal of Dynamics and Differential Equations, 2014
In this paper, the author proves the existence of a global attractor for the weak semiflow of a Boissonade system with quadratic and cubic parameters. Also, the upper semicontinuity in the \(H^1\) product space is proved, using uniform estimates with respect to the parameter.
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Synchronization, attractor fission, and attractor fusion in a globally coupled laser system

Physical Review A, 1992
A globally coupled class-B laser array with incoherent feedback is proposed for exploring the complex dynamics of dynamical systems with the highest connectivity. This feedback shows a fundamental characteristic, information lag, and results in the general features of synchronization, attractor fission, and attractor fusion processes.
, Otsuka, , Chern
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Compact Global Attractors

2020
The second chapter of this book is dedicated to the study of different kinds of dissipativity for dynamical systems (both autonomous and nonautonomous): point, compact, local, bounded, and weak. Criteria for point, compact, and local dissipativity are given.
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Global Attractor of One Nonlinear Parabolic Equation

Ukrainian Mathematical Journal, 2003
Let \(\Omega \) be a domain in \(\mathbb R^n\) with smooth boundary \(\partial \Omega \), \(\Omega_T:=[0,T]\times \Omega \). The authors consider the Cauchy-Dirichlet problem \[ \begin{gathered} u_t=a\Delta u-f(u)+\lambda u+\langle {\mathbf b}({\mathbf x}),\nabla u \rangle -g({\mathbf x});\tag{1} \\ u\big|_{\partial \Omega}=0,\quad u\big|_{t=0}=u_0 ...
Kapustyan, O. V., Shkundin, D. V.
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Global attractors and bifurcations

1996
We present some recent developments in the study of attractors of smooth dynamical systems, specially attractors whose basin has a global character. A key point in our approach is to explore the relations between this study and that of main bifurcation mechanisms.
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On the Theory of Global Attractors and Lyapunov Functionals

Set-Valued and Variational Analysis, 2012
This work is devoted to the study of the existence of global attractors for multivalued and single-valued semigroups, more specifically, under which conditions a multivalued (or single-valued) semigroup \(\{S(t): t\geqslant 0\}\) possesses a global attractor \(\mathcal{A}\).
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Global attractor for Hirota equation

Applied Mathematics-A Journal of Chinese Universities, 2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhang, Ruifeng, Guo, Boling
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Consequences Regarding the Global Attractor

1989
Let X be the global attractor of the dissipative system under consideration. Recall that X is the largest set in H with the properties (i) S(t)X = X for t ≥ 0, (ii) X is bounded in H, (iii) dist(S(t)uo,X) → 0 as t → ∞ for all uo ∈ H.
P. Constantin, C. Foias, B. Nicolaenko, R. Teman   +3 more
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Global attractors for autonomous evolution equations

2012
Chapter 2 is concerned with large time behaviour of solutions of evolution equations in terms of the global attractor, its existence and properties. Note that, good estimates on the dimension of attractors in terms of biological (medical, physical etc.) parameters are crucial for the finite-dimensional reduction and at present there exists a highly ...
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