Delay-independent design for chaotic synchronization in delay-coupled Bernoulli map networks

Abstract

The present paper considers chaotic synchronization in a network consisting of Bernoulli maps with a time-delay connection. We demonstrate that a connection strength and a map parameter at which chaotic synchronization occurs can be systematically designed, even for cases in which the connection delay, the number of maps, and the detailed topology information are unknown. The primary advantage of the proposed design is that the designed connection strength and map parameter are valid for any connection delay. This result is due to the fact that the stability of the synchronized state is the same as that of a time-invariant linear system having both an uncertain dimension and an uncertain parameter. For such a linear system, it is quite difficult to obtain the necessary and sufficient condition of the stability. However, a simple sufficient condition enables us to provide the design. The analytical results are confirmed through numerical examples.