Abstract: This paper presents a rigorous mathematical analysis of a two-species chemotaxis-competition model on weighted networks, incorporating nonlinear degenerate chemotactic sensitivities and volume-filling effects. The aim is to understand long-term population dynamics in networked environments. Using a Lyapunov functional approach, we characterize the asymptotic behavior of solutions. Under weak competition, coexistence occurs with exponential convergence, while strong competition leads to the extinction of one species and algebraic convergence to a segregated state. These theoretical results are validated through numerical simulations that highlight the effects of competition parameters, network topology, and initial conditions. The proposed numerical scheme demonstrates convergence with exponential or algebraic decay of relative errors, in agreement with the analytical results. This study highlights the role of network structure in shaping chemotaxis-driven competitive dynamics.

Keywords: Two-species Chemotaxis models, Competitive Interspecies, Asymptotic behaviour, Volume-filling effects, Weighted networks, Exponential and algebraic decay

Pages: 67-77