Adaptive synchronization of Lü system with uncertain parameters
type: Item
instance of: scholarly article
title: Adaptive synchronization of Lü system with uncertain parameters
zbMATH Open document ID: 1062.34039
published in: Chaos, Solitons and Fractals
publication date: 2004-08-19T00:00:00Z
review text: The paper addresses the problem of complete synchronization of two systems \(dx/dt=f(x)\), \(dy/dt=f(y)+g(x-y)\), where \(x,y\in \mathbb{R}^3\), \(f,g: \mathbb{R}^3\to \mathbb{R}^3\) are smooth functions. The right-hand side \(f(x)\equiv(a(x_2-x_1),-x_1 x_3 +c x_2, x_1 x_2 - x_3)^T\) corresponds to the Lü system, which was suggested in [Int. J. Bifurcation Chaos Appl. Sci. Eng. 12, 659--661 (2002; Zbl 1063.34510)]. The parameter \(a\) is assumed to be unknown. The authors suggest a control law, i.e., a function \(g\), and a parameter update law \(da/dt\) such that the systems are synchronized, that is, \(| x(t)-y(t)| \to 0\) as \(t\to \infty\) for all initial conditions.
reviewed by: S. Yanchuk
Mathematics Subject Classification ID: 34C15
Mathematics Subject Classification ID: 34D05
Mathematics Subject Classification ID: 34D23
Mathematics Subject Classification ID: 34C28
zbMATH DE Number: 2093271
zbMATH Keywords: Lü system
zbMATH Keywords: adaptive synchronization
zbMATH Keywords: uncertain parameters
zbMATH Keywords: chaotic attractor
author: E. M. Elabbasy
author: H. N. Agiza
author: M. M. El-Dessoky
MaRDI profile type: Publication
full work available at URL: j.chaos.2003.12.028
OpenAlex ID: W2084664131
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DOI: 10.1016/J.CHAOS.2003.12.028
description: scientific article; zbMATH DE number 2093271