Globally coupled multiattractor maps : mean field dynamics controlled by the number of elements

Abstract

We report an investigation of a system of N globally coupled maps able to support multiattractors. For these systems the mean field dynamics is controlled by the number of elements in the initial partition of each basin of attraction. This behavior is in strong contrast with coupled systems of maps with a single attractor, where the mean field dynamics is usually simple for weak couplings. In spite of the increased local complexity, the global dynamics can be reduced to a simple two-dimensional map up to the first bifurcation point of the coexisting attractors. [S1063-651X(99)50601-6].