Sharp Rate of the Accelerating Propagation for a Recursive System

ABSTRACT How to characterize the rate of accelerating propagation in recursive systems is a challenging topic though it has attracted great attention of theoretical and empirical ecologists. In this paper, we determine the sharp rate of accelerating propagation for a unimodal recursive system with a heavy‐tailed dispersal kernel through tracking of level sets of solutions with compactly supported initial data. It turns out that the solution level set satisfies for large , where is the level and is determined by the linearized system at zero.