Modeling the role of diffusion coefficients on Turing instability in a reaction-diffusion prey-predator system

The paper is concerned with the effect of variable dispersal rates on Turing instability of a non-Lotka-Volterra reaction-diffusion system. In ecological applications, the dispersal rates of different species tends to oscillate in time. This oscillation is modeled by temporal variation in the diffusion coefficient with large as well as small periodicity. The case of large periodicity is analyzed using the theory of Floquet multipliers and that of the small periodicity by using Hill's equation. The effect of such variation on the resulting Turing space is studied. A comparative analysis of the Turing spaces with constant diffusivity and variable diffusivities is performed. Numerical simulations are carried out to support analytical findings.