The dynamics of a symmetric coupling of three modified quadratic maps

doi:10.1088/1674-1056/22/8/080202

Abstract We investigate the dynamical behavior of a symmetric linear coupling of three quadratic maps with exponential terms, and identify various interesting features as a function of two control parameters. In particular, we investigate the emergence of quasiperiodic states arising from Naimark-Sacker bifurcations of stable period-1, period-2, and period-3 orbits. We also investigate the multistability in the same coupling. Lyapunov exponents, parameter planes, phase space portraits, and bifurcation diagrams are used to investigate transitions from periodic to quasiperiodic states, from quasiperiodic to mode-locked states and to chaotic states, and from chaotic to hyperchaotic states.

Keywords: Naimark-Sacker bifurcation quasiperiodicity chaos hyperchaos

Received: 22 October 2012
Revised: 26 January 2013
Accepted manuscript online:

PACS:	02.30.Rz	(Integral equations)
	05.45.-a	(Nonlinear dynamics and chaos)

Fund: Project supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico-CNPq, Brazil.

Corresponding Authors: Paulo C. Rech
E-mail: dfi2pcr@joinville.udesc.br

Cite this article:

Paulo C. Rech The dynamics of a symmetric coupling of three modified quadratic maps 2013 Chin. Phys. B 22 080202

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