Wave propagation in predator prey systems

       Prof. Je-Chiang Tsai  Taiwan Normal University

Abstract: We study a class of predator–prey systems of reaction–diffusion type. Specifically, we are interested in the dynamical behaviour for the solution with the initial distribution where the prey species is at the level of the carrying capacity, and the density of the predator species has compact support, or exponentially small tails at two ends.  Numerical evidence suggests that this will lead to the formation of a pair of diverging waves propagating outwards from the initial zone. Motivated by this phenomenon, we establish the existence of a family of travelling waves with the minimal speed, and compute the spreading speed of the predator species for a class of biologically acceptable initial distributions.