Continuous and discrete periodic asymptotic behavior of solutions to a competitive chemotaxis PDEs system

摘要

In this paper we study the continuous and full discrete versions of a parabolic-parabolicelliptic system with periodic terms that serves as a model for some chemotaxis phenomena. This model appears naturally in the interaction of two biological species and a chemical. The presence of the periodic terms has a strong impact on the behavior of the solutions. Some conditions on the system's data are given that guarantee the global existence of solutions that converge to periodical solutions of an associated ODE's system. Further, we analyze the discretized version of the model using a Generalized Finite Difference Method (GFDM) and we confirm that the properties of the continuous model are also preserved for the resulting discrete model. To this end, we prove the conditional convergence of the numerical model and study some practical examples. (C) 2020 Published by Elsevier B.V.