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Title: Dislocated negative feedback control with partial replacement between chaotic Lorenz systems
Authors: Laureano, Rosário D.
Mendes, Diana A.
Ferreira, Manuel Alberto M.
Keywords: Asymptotical chaos synchronization
Negative feedback control
Chaotic Lorenz system
Unidirectional coupling
Global stability
Lyapunov direct method
Issue Date: 2013
Publisher: Hilaris
Abstract: In order to obtain asymptotical synchronization, we combine negative feedback control and dislocated negative feedback control with partial replacement to the nonlinear terms of the response system, a coupling version that was less explored. All these unidirectional coupling schemes are applied between Lorenz systems where we consider some values for the control parameters that lead to chaotic behavior. The sufficient conditions for global stable synchronization are obtained from a different approach of the Lyapunov direct method for the transversal system. In one of the coupling we apply a result based on the classification of the symmetric matrix AT +A as negative definite,where A is characterizing the transversal system. In the other couplings presented here, the sufficient conditions are based on the derivative increase of an appropriate Lyapunov function. In fact, the effectiveness of the coupling between systems with equal dimension follows from the analysis of the synchronization error, e(t), and, if the system variables can be bounded by positive constants, then the derivative of an appropriate Lyapunov function can be increased as required by the Lyapunov direct method.
Peer reviewed: Sim
ISSN: 1314-3336
Publisher version: The definitive version is available at:
Appears in Collections:DM-RI - Artigos em revistas científicas internacionais

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MAMFerreira 2013 Mathematica Aeterna 3(5)337-348.pdf173.85 kBAdobe PDFView/Open

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