An Interdisciplinary Journal

2008, Vol.11, No.2, pp.233-240

A Method for Studying the Stability and the Existence of Discrete Breathers in a Chain of Coupled Symplectic Maps.
V. Koukouloyannis, Th. Tziotzios, and G. Voyatzis

A one-dimensional chain of weakly coupled symplectic maps is studied. We examine the existence and the size of the stability regions around specific periodic orbits in the phase space of the system with respect to the length of the chain and the coupling strength between the oscillators. In order to accomplish this, we consider a set of orbits defined by a grid of initial conditions in a proper section of the phase space of the system and classify them according to their regularity using the fast Lyapunov indicator (FLI) as a chaos indicator. The correlation between the existence of stability islands and the linear stability of the corresponding periodic orbits is demonstrated. The results of our study are used in order to examine the stability properties of Discrete Breathers (DBs) i.e. spatially localized oscillations in extended systems. Finally, we illustrate how this method can be used in order to indicate the existence of DBs and other breather-like motions.
Key words: breather-like motion, coupled symplectic maps, Lyapunov indicator

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