Spatio-temporal chaos for the Gray-Scott model

A new geometrical criterion for the transition to spatio-temporal chaos (STC) arising in the Gray-Scott model is presented. This is based on the inter-relationship of global bifurcating branches of ordered patterns with respect to supply and removal rates contained in the model. This viewpoint not only gives us a new criterion for the onset of STC but also clarifies how the orbit itinerates among several ordered patterns in infinite-dimensional space. Moreover, the geometrical characterization gives us a universal viewpoint about the onset and termination of STC. There are at least two different mechanisms that cause re-injection dynamics and drive the STC: one is a generalized heteroclinic cycle consisting of self-replication and self-destruction processes, and the other involves annihilation of colliding waves instead of self-destruction. (C) 2001 Elsevier Science B.V. All rights reserved.