Paper Info
Title
Synchronization And Basins Of Synchronized States In Two-Dimensional Piecewise Maps Via Coupling Three Pieces Of One-Dimensional Maps
Abstract
This paper is devoted to the synchronization of a dynamical system defined by two different coupling versions of two identical piecewise linear bimodal maps. We consider both local and global studies, using different tools as natural transversal Lyapunov exponent, Lyapunov functions, eigenvalues and eigenvectors and numerical simulations. We obtain theoretical results for the existence of synchronization on coupling parameter range. We characterize the synchronization manifold as an attractor and measure the synchronization speed. In one coupling version, we give a necessary and sufficient condition for the synchronization. We study the basins of synchronization and show that, depending upon the type of coupling, they can have very different shapes and are not necessarily constituted by the whole phase space; in some cases, they can be riddled.
Year
DOI
Venue
2013
10.1142/S0218127413501344
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
Keywords
DocType
Volume
Almost global synchronization, Lyapunov exponents, basins, Lyapunov functions
Journal
23
Issue
ISSN
Citations 
8
0218-1274
0
PageRank 
References 
Authors
0.34
0
5
Name
Order
Citations
PageRank
Daniele Fournier-Prunaret112820.38
J. Leonel Rocha245.33
Acilina Caneco310.72
Sara Fernandes400.34
Clara Grácio542.32