Reaction-diffusion (RD) equations are commonly used to describe the propagation effects in population interactions in ecology. RD system are described by parabolic partial differential equations (PDE), based on the Fick diffusion equation, hence arbitrary large population speeds are involved. To avoid this unrealistic situation, we introduce the Cattaneo's diffusion in spatiotemporal models of prey-predator interactions, which leads to more realistic and interesting interactions between populations and can be useful to gain insights to the understanding of food-chain dynamics. The resulting model is the so-called telegraph RD model. Numerical simulations on a predator-prey model with Holling type II functional response and cross-diffusion show the effects of the relaxation time in the dynamic of population interactions.
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