Finite element analysis of the nonlocal diffusion effect in a two-species chemotaxis system

This research delves into the analysis of the boundness solution for a two-species chemotaxis system with nonlocal diffusion. Initially, the two-species chemotaxis (TSC) system is represented by a set of partial differential equations with Neumann boundary conditions. Based on the assumptions, necessary and sufficient conditions are derived for ensuring the unique global bounded solution of the proposed TSC system under nonlocal diffusion. In this study, the proposed system's boundness conditions are also derived for two different cases. Finally, we present the numerical simulation results based on system parameter values, demonstrating the effectiveness of the nonlocal diffusion in the TSC system.