Synergistic regulation of spatiotemporal pattern formation by inertial times and fitness taxis

This study explores the mechanism of pattern formation in a hyperbolic reaction-diffusion system that incorporates fitness taxis of species. Through rigorous mathematical derivation, we have established the conditions for Turing instability and wave instability, where the inertial motion of species and fitness taxis collectively regulate complex spatiotemporal behavior. To confirm the theoretical findings, we revealed the hierarchical structure of non-equilibrium dynamics through numerical simulations and demonstrated how inertial effects and fitness taxis synergistically drive different dynamics in the reaction-diffusion framework.