ROUTE TO CHAOS FOR A GLOBAL VARIABLE OF A 2-DIMENSIONAL GAME-OF-LIFE TYPE AUTOMATA NETWORK

We consider a two-dimensional cellular automaton whose rule consists o f two subrules. The first, applied synchronously, is a local rule insp ired from the 'game of life', with a larger neighbourhood. The second, applied sequentially, describes the motion of a fraction rn of indivi duals. Such rules appear to be useful for modelling complex systems in ecology, such as natural populations of animals, in which the motion of the individuals is believed to play an important role. If the motio n is long-range, the density of individuals exhibits a sequence of per iod-doubling bifurcations and behaves chaotically when m is large enou gh. If the motion is short-range (i.e. restricted to first neighbours) , patterns become inhomogeneous. Spatial correlations decay with a fin ite correlation length xi of the order of root m. We observe the forma tion of domains, of mean width xi, with a chaotic behaviour of the loc al density of individuals, but the collective behaviour is stationary (the global density tends to a fixed value when the lattice size is mu ch larger than xi x xi).