Complex Dynamical Analysis of Two Prey−One Predator Model in a Patch Environment Utilizing Spectral Bound

In this article, a two prey-one predator model in which prey and predator disperse simultaneously in a heterogeneous environment with n patches is proposed and analyzed. We prove that the solution of the system is positive and uniformly ultimately bounded. Meanwhile, we use the monotonic theory of spectral bounds to investigate the effect of the dispersal rate on population dynamics. To be precise, we discuss the stability behaviour for the trivial equilibrium and semitrivial equilibrium as well as the uniform persistence of the system. Furthermore, we prove the global asymptotic stability of the positive equilibrium by constructing a global Lyapunov function which applies the results from graph theory. Some numerical simulations are provided to show the effectiveness of the theoretical results.