Abstract
A reaction–diffusion system with nonlinear–nonlocal functional response is considered in this article. We develop the finite delays approximation method combining with the spreading speed and travelling wavefronts theory for semi-flow to discuss the existence of spreading speed c∗ and travelling wavefronts without the differentiability assumption on the reaction function f . The asymptotic patterns and threshold property for the solutions of the considered system are described clearly according to the threshold parameter c∗ which is exactly the minimal wave speed as well. Finally, we give an estimate of the spreading speed and minimal wave speed c∗.
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