T. Killingback et M. Doebeli, SELF-ORGANIZED CRITICALITY IN SPATIAL EVOLUTIONARY GAME-THEORY, Journal of theoretical biology, 191(3), 1998, pp. 335-340
Self-organized criticality is an important framework for understanding
the emergence of scale-free natural phenomena. Cellular automata prov
ide simple interesting models in which to study self-organized critica
lity. We consider the dynamics of a new class of cellular automata whi
ch are constructed as natural spatial extensions of evolutionary game
theory. This construction yields a discrete one-parameter family of ce
llular automata. We show that there is a range of parameter values for
which this system exhibits complex dynamics with long range correlati
ons between states in both time and space. In this region the dynamics
evolve to a self-organized critical state in which structures exist o
n all time and length scales, and the relevant statistical measures ha
ve power law behaviour. (C) 1998 Academic Press Limited.