Spatiotemporal pattern induced by self and cross-diffusion in a spatial Holling-Tanner model

Abstract

In this paper, we have made an attempt to provide a unified framework to understand the complex spatiotemporal patterns induced by self and cross diffusion in a spatial Holling-Tanner model forphytoplankton-zooplankton-fish interaction. The effect of critical wave length which can drive the system to instability is investigated. We have examined the criterion between two cross-diffusivity (constant and timevarying)on the stability of the model system and for diffusive instability to occur. Based on these conditions and by performing a series of extensive simulations, we observed the irregular patterns, stationary strips, spots, and strips-spots mixture patterns. Numerical simulation results reveal that the regular strip-spot mixture patterns prevail over the whole domain on increasing the values of self- diffusion coefficients of phytoplankton and zooplankton and the dynamics of the system do not undergo any further changes.

Keywords

• spatiotemporal pattern
• diffusion
• Holling-Tanner model
• phytoplankton-zooplankton-fish interaction