Synchronization of chaotic systems by linear feedback controller
type: Item
instance of: scholarly article
title: Synchronization of chaotic systems by linear feedback controller
zbMATH Open document ID: 0923.34050
DOI: 10.1016/S1007-5704(98)90055-7
author: Zhenxun Huang
author: Jiong Ruan
published in: Communications in Nonlinear Science and Numerical Simulation
publication date: 1999-10-18T00:00:00Z
review text: Consider the coupled differential system \((*) \;dx/dt =f(x) + K(y-z), dy/dt=g(y)\) with \(x,y\in \mathbb{R}^n\), \(f(0)=g(0)=0\), \(K= \text{diag} (k_1 , \dots , k_n)\). Let \(\overline{y} (t)\) be a global solution to \(dy/dt=g(y)\) satisfying \(| \overline{y} (t)| \leq M\) for \( t\geq 0\). Under the assumptions \(f(x) \equiv g(x)\), \(K = kI\) where \(I\) is the \(n\times n\)-identity matrix, the authors derive two conditions each of them guaranteeing \(\lim_{t \rightarrow +\infty} \| x(t)- \overline{y} (t)\|=0\) for any solution \((x(t), \overline{y} (t))\) to \((*)\). They prove a negative result on the synchronizability of \((*)\) in case \(f\neq g\).
Mathematics Subject Classification ID: 34D05
Mathematics Subject Classification ID: 93B52
Mathematics Subject Classification ID: 34H05
zbMATH DE Number: 1286579
zbMATH Keywords: synchronization
zbMATH Keywords: chaotic behavior
zbMATH Keywords: linear feedback controller
reviewed by: Klaus R. Schneider
MaRDI profile type: Publication
cites work: Controlling chaos
cites work: On the control of complex dynamic systems
cites work: On feedback control of chaotic continuous-time systems
cites work: TRANSITIONS IN DYNAMICAL REGIMES BY DRIVING: A UNIFIED METHOD OF CONTROL AND SYNCHRONIZATION OF CHAOS
cites work: Q5822590
cites work: Q3871201
full work available at URL: s1007-5704(98)90055-7
OpenAlex ID: W2032795939
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description: scientific article; zbMATH DE number 1286579