A stage structured predator-prey model with periodic orbits

Abstract

<p style='text-indent:20px;'>This paper studies the existence and multiplicity of periodic orbits of a stage-structured predator-prey model with Beddington-DeAngelis functional response. We derive an existence criterion of periodic orbit in terms of inequalities of system's nine parameters and prove that the system admits at least two limit cycles or three limit cycles via subcritical Hopf bifurcation or generalized Hopf bifurcation theory and hypersurface theory. We also prove that each one-parameter system possesses at least one limit cycle when it is larger or smaller than its Hopf bifurcating value, or between its Hopf bifurcating values. Combining theoretic analysis and numerical simulations, we investigate global bifurcations of limit cycles for a varying parameter system, which provides a plenty of bifurcating properties and again suggests that the system has at least three limit cycles. Similar results are obtained for the system without mutual interference.</p>