SPATIAL PATTERNS IN POPULATION CONFLICTS

We consider a dynamical model for evolutionary games, and enquire how the introduction of diffusion may lead to the formation of stationary spatially inhomogeneous solutions, that is patterns. For the model equ ations being used it is already known that if there is an evolutionari ly stable strategy (ESS), then it is stable. Equilibrium solutions whi ch are not ESS's and which are stable with respect to spatially consta nt perturbations may be unstable for certain choices of the dispersal rates. We prove by a bifurcation technique that under appropriate cond itions the instability leads to patterns. Computations using a curve-f ollowing technique show that the bifurcations exhibit a rich structure with loops joined by symmetry-breaking branches.