Hölder continuity of three types of generalized synchronization manifolds of non-autonomous systems
type: Item
instance of: scholarly article
title: Hölder continuity of three types of generalized synchronization manifolds of non-autonomous systems
zbMATH Open document ID: 1195.34073
author: Aihua Hu
author: Zhenyuan Xu
author: Liuxiao Guo
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2009-12-18T00:00:00Z
review text: The paper considers the following non-autonomous unidirectionally coupled systems \[ \frac{dy}{dt}=g(t,y), \quad \frac{dx}{dt}=Ax +f(t,x) + K (y-x), \] where \(x,y\in\mathbb{R}^n\), \(f(t,y)\) and \(f(t,x)\) are smooth functions, and \(A\), \(K\) are \(n\times n\) constant matrices. For the cases, when the modified response system \[ \frac{dx}{dt}=Ax +f(t,x) - K x \] has an asymptotically stable equilibrium, periodic, or quasiperiodic attractor, sufficient conditions for the existence of Hölder continuous invariant manifold \(S=\{ (t,x,y): x=\Phi(t,y) \}\) are given. The manifold \(S\) is called the generalized synchronization manifold.
reviewed by: S. Yanchuk
Mathematics Subject Classification ID: 34D06
Mathematics Subject Classification ID: 34C15
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34C45
Mathematics Subject Classification ID: 34D35
zbMATH DE Number: 5649935
zbMATH Keywords: generalized synchronization manifold
zbMATH Keywords: non-autonomous systems
zbMATH Keywords: Hölder continuity
zbMATH Keywords: Schauder fixed point theorem
MaRDI profile type: Publication
full work available at URL: j.na.2009.04.068
OpenAlex ID: W1985673342
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DOI: 10.1016/J.NA.2009.04.068
description: scientific article; zbMATH DE number 5649935