Spatiotemporal dynamics analysis of a discrete model of <i>Aphis gossypii</i> Glover and <i>Coccinella undecimpunctata</i> Linnaeus with cross-diffusion and advection

In this paper, we present a novel spatiotemporal discrete model for Aphis gossypii Glover and Coccinella undecimpunctata Linnaeus, incorporating the effects of cross-diffusion and advection. Utilizing a coupled mapping lattice approach, we construct this model to explore the intricate dynamics of these species. Initially, we analyze the stability of the equilibrium point in the absence of diffusion and advection, investigating the conditions for the occurrence of Flip bifurcation and Neimark–Sacker bifurcation, along with their normal forms. Upon introducing cross-diffusion, we observe distinct bifurcation behaviors and Turing patterns in the populations of A. gossypii, influenced by varying diffusion coefficients. Furthermore, our examination of advection effects reveals that as the advection coefficient increases, the corrugated spatial patterns in the horizontal direction become increasingly pronounced, highlighting the complex interplay between these factors. All theoretical findings are substantiated by comprehensive numerical simulations, reinforcing the robustness of our model. Additionally, we delve into the biological implications of our results, offering insights into the ecological dynamics of these species and potential strategies for effective biological control.