Treffer: 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 J$J$ through tracking of level sets of solutions with compactly supported initial data. It turns out that the solution level set Eλ(n)$E_{\lambda }(n)$ satisfies J(Eλ(n))∼e−ρ∗n$J(E_\lambda (n))\sim e^{-\rho ^* n}$ for large n$n$, where λ$\lambda$ is the level and ρ∗$\rho ^*$ is determined by the linearized system at zero. [ABSTRACT FROM AUTHOR]

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