The Dynamics of a Nonlocal Dispersal Logistic Model with Seasonal Succession and Free Boundaries.

This paper is devoted to a nonlocal dispersal logistic model with seasonal succession and free boundaries, where the free boundaries represent the expanding front and the seasonal succession accounts for the effect of two different seasons. Technically, this free boundary problem is much more difficult than the case without seasonal succession since the coefficients are all time periodic and piecewise continuous. We prove the existence and uniqueness of global solution, and then examine the long-time dynamical behaviour and the criteria that completely determine when spreading and vanishing can happen, revealing some significant differences from the model without seasonal succession. Moreover, we use a "thin-tail" condition on the kernel function to estimate the asymptotic speeds of (g, h) and the asymptotic spreading speed of u, which is achieved by solving the associated semi-wave problem. [ABSTRACT FROM AUTHOR]