A simple way to compute the existence region of 1D chaotic attractors in 2D-maps

We study a new approach to computing the existence region of self-synchronized states in the error feedback synchronization scheme for discrete-time chaotic systems. The overall system is modelled by a triangular 2D-map in which the nonlinearity is a symmetric tent map. We compute the stability region D-c of one dimensional chaotic attractors using the boundaries in the bifurcation diagram of the 1D-symmetric tent map, also called critical lines. We show that with a modest number of these critical lines (about 16), the approximation of D-c is quite accurate.