Negreanu, MihaelaVargas Ureña, Antonio Manuel2025-01-102025-01-102021-04Negreanu, M. & Vargas A.M. (2021). Continuous and discrete periodic asymptotic behavior of solutions to a competitive chemotaxis PDEs system. Communications in Nonlinear Science and Numerical Simulation, 95. https://doi.org/10.1016/J.CNSNS.2020.1055921007-5704 | eISSN 1878-7274https://doi.org/10.1016/j.cnsns.2020.105592https://hdl.handle.net/20.500.14468/25173This is a Submitted Manuscript of an article published by Elsevier in "Communications in Nonlinear Science and Numerical Simulation, 95, 105592", available at: https://doi.org/10.1016/j.cnsns.2020.105592Este es el manuscrito enviado del artículo publicado por Elsevier en "Communications in Nonlinear Science and Numerical Simulation, 95, 105592", disponible en línea: https://doi.org/10.1016/j.cnsns.2020.105592In this paper we study the continuous and full discrete versions of a parabolic-parabolic-elliptic 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.eninfo:eu-repo/semantics/openAccess12 MatemáticasartículoChemotaxisAsymptotic stability of solutionsLotka Volterra systemPeriodic solutionsGeneralized Finite Di erenceMethodConditional Convergence