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Title: Efficient synchronization of one-dimensional chaotic quadratic maps by different couling terms
Authors: Laureano, M.
Mendes, D. A.
Ferreira, M. A. M.
Keywords: Efficient synchronization
One-dimensional chaotic quadratic maps
Different coupling terms
Issue Date: 2010
Publisher: Progress IPS LLC
Abstract: The possibility of chaotic systems oscillate in a coherent and synchronized way is not an obvious phenomenon, since it is not possible to reproduce exactly the initial conditions and the sensitive dependence on initial conditions is one of the main characteristics associated with the chaotic behavior. We consider synchronization phenomena of discrete chaotic dynamical systems (identical or non-identical) with nonlinear unidirectional and bidirectional coupling schemes. In order to illustrate the synchronization methods present in this paper, we always use a system of two coupled chaotic quadratic maps. First, we present a systematic way to design unidirectional and bidirectional coupling schemes for synchronizing arbitrary pairs of one-dimensional chaotic maps. In dissipative coupling, we use two methods to study the stability of synchronous state: the linear stability and the Lyapunov functional analysis. Second, we explore other coupling schemes. With the unidirectional coupling based on the singular value decomposition it is possible to suppress the exponential divergence of the dynamics of the synchronization error and to guarantee linear stability of the synchronized state in all points of the state space. The other coupling scheme is asymmetric and appears in natural a family of analytic complex quadratic maps.
Peer reviewed: yes
ISSN: 2078-0257
Appears in Collections:BRU-RI - Artigos em revistas científicas internacionais com arbitragem científica

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