The present Letter proposes a design procedure for inducing synchronization in delayed-coupled one-dimensional map networks. We assume the practical situation where the connection delay, the detailed information about the network topology, and the number of the maps are unknown in advance. In such a situation, it is difficult to guarantee the stability of synchronization, since the local stability of a synchronized manifold is equivalent to that of a linear time-variant system. A sufficient condition in robust control theory helps us to derive a simple design procedure. The validity of our design procedure is numerically confirmed.

A numerical method is presented for calculating transverse and non-transverse (or tangent) types of homoclinic points of a two-dimensional noninvertible map having an invariant set that reduces to a one-dimensional noninvertible map. To illustrate bifurcation diagrams of homoclinic points and transitions of chaotic states near the bifurcation parameter values, three systems including coupled chaotic maps are studied.

We propose an equivalent circuit model described by the Rössler equation. Then we can consider a coupled Rössler system with a physical meaning on the connection. We consider an oscillatory circuit such that two identical Rössler circuits are coupled by a resistor. We have studied three routes to entirely and almost synchronized chaotic attractors from phase-locked periodic oscillations. Moreover, to simplify understanding of synchronization phenomena in the coupled Rössler system, we investigate a mutually coupled map that shows analogous locking properties to the coupled Rössler System.