Dynamical analysis, feedback control and synchronization of Liu dynamical system
type: Item
instance of: scholarly article
title: Dynamical analysis, feedback control and synchronization of Liu dynamical system
zbMATH Open document ID: 1176.34060
author: B. E. Eshmatov
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2008-11-20T00:00:00Z
review text: Subject of the paper is the Liu system of scalar ordinary differential equations \[ x'=a(x-y),\quad y'=bx-kxz, \quad z'=-cz+hx^2, \] where \(a,b,c,k,h\) are real parameters. The paper investigates the local dynamics in the vicinity of equilibria of this system. In particular, conditions for stability of equilibria and Hopf bifurcations are obtained. Using center manifold theory, criticality of the Hopf bifurcation is investigated (supercritical or subcritical). Linear feedback control is applied to stabilize and synchronize two Liu systems.
reviewed by: S. Yanchuk
Mathematics Subject Classification ID: 34D05
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 93D15
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C28
Mathematics Subject Classification ID: 34H05
zbMATH DE Number: 5369410
zbMATH Keywords: Liu system
zbMATH Keywords: stability
zbMATH Keywords: Hopf bifurcation
zbMATH Keywords: linear feedback control
zbMATH Keywords: supercrtitical (subcritical) bifurcation
MaRDI profile type: Publication
full work available at URL: j.na.2007.09.029
OpenAlex ID: W2056525521
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DOI: 10.1016/J.NA.2007.09.029
description: scientific article; zbMATH DE number 5369410