Instability and irregular behavior of coupled logistic equations

We analyze some general features of two models of coupled logistic equations. We find that, for selected values of the three control parameters, chaotic patterns may emerge out of an infinite sequence of period-doubling bifurcations. However, there exist large regions of control-parameter space where the approach to irregular behavior appears to be consistent with the Newhouse-Ruelle-Takens scenario, as evidenced by the appearance of two characteristic frequencies. As the ratio of these frequencies is varied, by changing the control parameters, phase locking and quasiperiodic motion are observed on the way to chaos.