Cross-Diffusion-Driven Instability in a Reaction-Diffusion Harrison Predator-Prey Model

Abstract EN

We present a theoretical analysis of processes of pattern formation that involves organisms distribution and their interaction of spatially distributed population with cross-diffusion in a Harrison-type predator-prey model.

We analyze the global behaviour of the model by establishing a Lyapunov function.

We carry out the analytical study in detail and find out the certain conditions for Turing’s instability induced by cross-diffusion.

And the numerical results reveal that, on increasing the value of the half capturing saturation constant, the sequences “spots → spot-stripe mixtures → stripes → hole-stripe mixtures → holes” are observed.

The results show that the model dynamics exhibits complex pattern replication controlled by the cross-diffusion.