Cross-diffusion-driven instability in a reaction-diffusion Harrison predator-prey model
Summary: 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 \(\rightarrow \) spot-stripe mixtures \(\rightarrow\) stripes \(\rightarrow\) hole-stripe mixtures \(\rightarrow \) holes'' are observed. The results show that the model dynamics exhibits complex pattern replication controlled by the cross-diffusion.
scientific article; zbMATH DE number 6161320