Spatio-temporal chaos for the Gray-Scott model

A new geometrical criterion for the transition to spatio-temporal chaos (ST C) arising in the Gray-Scott model is presented. This is based on the inter -relationship of global bifurcating branches of ordered patterns with respe ct to supply and removal rates contained in the model. This viewpoint not o nly gives us a new criterion for the onset of STC but also clarifies how th e orbit itinerates among several ordered patterns in infinite-dimensional s pace. Moreover, the geometrical characterization gives us a universal viewp oint about the onset and termination of STC. There are at least two differe nt mechanisms that cause re-injection dynamics and drive the STC: one is a generalized heteroclinic cycle consisting of self-replication and self-dest ruction processes, and the other involves annihilation of colliding waves i nstead of self-destruction. (C) 2001 Elsevier Science B.V. All rights reser ved.