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