Dynamic characteristics of a hyperbolic reaction-diffusion predator-prey system with self-diffusion and nonidentical inertia

Hyperbolic reaction-diffusion (HRD) systems have emerged as a better descriptor of the macroscopic spatial interaction models used for studying pattern formation in chemical and biological systems. In contrast to the parabolic reaction-diffusion (PRD) models, the spatial disturbances in an HRD system travel through space with finite velocity. This paper considers the simplest two-species HRD model with different inertia based on the telegraph equation. The underlying reaction terms are considered as a predator-prey interaction with type III response function and prey refuge. We prescribe the analytical conditions for the existence of diffusion-driven instabilities of the considered system. Simulation results further verify the theoretical results. A connection between the refuge parameter and inertial time is discussed in generating different spatiotemporal patterns. Extension of the two-species PRD system to HRD system with diagonal diffusion matrix causes a diffusion-driven wave instability, which is never possible for its parabolic counterpart. Furthermore, the patterns under pure wave instability are dependent on the initial population density.