Synchronization in ensembles of coupled maps and
its application to
information processing
M.E. Shirokov, S.O. Starkov
Institute of Radio Engineering and Electronics
of the Russian Academy
of Sciences, Moscow, Russia
We consider ensembles consisting of arbitrary number of locally and globally coupled maps. The aim of our research is to investigate a possibility of chaotic synchronization in such ensembles in the following sense. We use the term ''synchronization'' for such a dynamical regime in the ensemble of coupled maps, in which the phase states of all the maps are equal to each other at any moment. It is shown that for the particular type of coupling the conditions of stability of synchronization state for small perturbations are defined by the value of the first Lyapunov exponent of the partial dynamics in each (isolated) map and spectral characteristics of the coupling matrix. The obtained results are applied to concrete ensembles of coupled maps.
With the aim to investigate the dynamics of the particular coupled maps structures the computer simulation using logistic maps and Henon maps as partial system was carried out. The computer simulation revealed a possibility of synchronization of the coupled maps in accordance with theoretical conditions and some properties of such a regime.
We consider applications of synchronization phenomenon to information processing. For example, we derive a procedure for retrieving information stored on unstable cycles of n-dimensional maps based on synchronization of such maps.
It is shown that the obtained results may also be used for experimental or numerical calculations of the first Lyapunov exponent of chaotic and nonchaotic regimes of discrete-time dynamical systems.