Dynamics of heterogeneous population due to spatially distributed parameters and an ideal free pair - Zahan, Ishrat; Kamrujjaman, Md.; Alim, Md. Abdul; Mohebujjaman, Muhammad; Khan, Taufiquar (Frontiers in Applied Mathematics and Statistics, 2022)
Population movements are necessary to survive the individuals in many cases and depend on available resources, good habitat, global warming, climate change, supporting the environment, and many other issues. This study explores the spatiotemporal effect on the dynamics of the reaction-diffusion model for two interacting populations in a heterogeneous habitat. Both species are assumed to compete for different fundamental resources, and the diffusion strategies of both organisms follow the resource-based diffusion toward a positive distribution function for a large variety of growth functions. Depending on the values of spatially distributed interspecific competition coefficients, the study is conducted for two cases: weak competition and strong competition, which do not perform earlier in the existing literature. The stability of global attractors is studied for different conditions of resource function and carrying capacity. We investigated that in the case of weak competition, coexistence is attainable, while strong competition leads to competitive exclusion. This is an emphasis on how resource-based diffusion in the niche impacts selection. When the natural resources are in sharing, either competition or predator-prey interaction lead to competitive exclusion or coexistence of competing species. However, we concentrate on the situation in which the ideal free pair is achieved without imposing any other additional conditions on the model's parameters. The effectiveness of the model is accomplished by numerical computation for both one and two space dimensions cases, which is very important for biological consideration.