We report exact analytical expressions locating the 0→1, 1→2 and 2→4 bifurcation curves for a prototypical system of two linearly coupled quadratic maps. Of interest is the precise location of the parameter sets where Naimark–Sacker bifurcations occur, starting from a non-diagonal...

By varying real parameters, unstable complex orbits may become stable over wide parameter ranges. Thus, phase diagrams obtained by analyzing solely the stability of real solutions may be incomplete.

We investigate the impact of bistability in the emergence of synchronization in networks of chaotic maps with delayed coupling. The existence of a single finite attractor of the uncoupled map is found to be responsible for the emergence of synchronization. No synchronization is observed when the...