Crisis-induced intermittency in coupled chaotic maps has been studied. Observation of qualitative changes in basin structure is useful for understanding global bifurcations in 1D and 2D systems. However, it is difficult in higher-dimensional systems. We have demonstrated that variation of fractal dimension of a basin boundary can provide information on a global bifurcation in 2D coupled chaotic maps. Moreover, the idea has been successfully applied to a chaotic neural network.
In higher-dimensional coupled chaotic maps, multiple attractors often coexist and a basin boundary is likely to be fractal due to its non-invertible nature. Hence, a crisis point inducing intermittency can be specified by failure of computation of fractal dimension. In this sense, the simple method is one of the approaches to understanding of a global bifurcation through a contact between a fractal basin boundary and attractors.
The author thank K. Aihara at University of Tokyo and T. Yoshinaga at University of Tokushima for helpful suggestions and useful discussions.