Intrinsically localized chaos in discrete nonlinear extended systems

¹ Group of Theory and Simulation of Complex Systems Departamento de Física Aplicada, CSIC-Universidad de Zaragoza E-50009 Zaragoza, Spain
² Group of Theory and Simulation of Complex Systems Departamento de Física de la Materia Condensada, CSIC-Universidad de Zaragoza E-50009 Zaragoza, Spain
³ Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology - Cambridge, MA 02319, USA

Received: 19 October 1998
Accepted: 16 December 1998

Abstract

The phenomenon of intrinsic localization in discrete nonlinear extended systems, i.e. the (generic) existence of discrete breathers, is shown to be not restricted to periodic solutions but to also extend to more complex (chaotic) dynamical behaviour. We illustrate this with two different forced and damped systems exhibiting this type of solutions: In an anisotropic Josephson junction ladder, we obtain intrinsically localized chaotic solutions by following periodic rotobreather solutions through a cascade of period-doubling bifurcations. In an array of forced and damped van der Pol oscillators, they are obtained by numerical continuation (path-following) methods from the uncoupled limit, where its existence is trivially ascertained, following the ideas of the anticontinuum limit.