Sharp Rate of the Accelerating Propagation for a Recursive System

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 (Formula presented.) through tracking of level sets of solutions with compactly supported initial data. It turns out that the solution level set (Formula presented.) satisfies (Formula presented.) for large (Formula presented.), where (Formula presented.) is the level and (Formula presented.) is determined by the linearized system at zero.