Pattern formation induced by fractional cross-diffusion in a 3-species food chain model with harvesting

Abstract

In this article, we explore the pattern formation caused by fractional cross-diffusion in a 3-species ecological symbiosis model with harvesting. Initially, all possible points of equilibrium are established and then by using Routh–Hurwitz criteria stability of an interior equilibrium point is explored. The conditions for Turing instability are obtained by local equilibrium points with stability analysis. In the neighborhood of the Turing bifurcation point weakly nonlinear analysis is used to deduce the amplitude equations. The conditions for the formation of the Turing patterns such as hexagons, rhombus, spots, squares, strips and waves patterns are identified for the amplitude equations through the dynamical analysis. Furthermore, by using the numerical simulations, the theoretical results are verified.