Benito, J. J.García, A.Gavete, L.Negreanu, MihaelaUreña, F.Vargas, A. M.2023-06-172023-06-1720212196-437810.1007/s40571-020-00359-whttps://hdl.handle.net/20.500.14352/7281This paper focuses on the numerical analysis of a discrete version of a nonlinear reaction–diffusion system consisting of an ordinary equation coupled to a quasilinear parabolic PDE with a chemotactic term. The parabolic equation of the system describes the behavior of a biological species, while the ordinary equation defines the concentration of a chemical substance. The system also includes a logistic-like source, which limits the growth of the biological species and presents a time-periodic asymptotic behavior. We study the convergence of the explicit discrete scheme obtained by means of the generalized finite difference method and prove that the nonnegative numerical solutions in two-dimensional space preserve the asymptotic behavior of the continuous ones. Using different functions and long-time simulations, we illustrate the efficiency of the developed numerical algorithms in the sense of the convergence in space and in time.engjournal articlehttps://doi.org/10.1007/s40571-020-00359-wopen access519.6Chemotaxis systemsGeneralized Finite differenceMeshless methodAsymptotic stabilityAnálisis numérico1206 Análisis Numérico