Global bifurcation in a dirichlet-boundary chemotactic predator-prey System

Abstract This study investigates the global bifurcation dynamics of coexistence states in a chemotactic predator-prey system under homogeneous Dirichlet boundary conditions. By unifying a priori estimates with the unilateral global bifurcation theorem, we rigorously characterize the existence and stability of positive solutions, revealing that Dirichlet constraints amplify the ecological impacts of trophic strategy differences. Numerical simulations validate theoretical thresholds for coexistence collapse, highlighting the coupling mechanism between boundary effects and foraging strategies. This work advances the mathematical theory of chemotaxis systems under Dirichlet constraints and provides actionable insights for biodiversity conservation in fragmented ecosystems.