Abstract
A stage structured prey predator system with modified Leslie-Gower scheme is presented, where both maturation delay for prey and gestation delay for predator are considered. By analyzing the associated characteristic transcendental equation, combined dynamic effects of stage structure and double time delays on population dynamics are discussed, and regions of local stability around interior equilibrium are studied. According to Hopf bifurcation theorem for functional differential equations, existence of Hopf bifurcation around interior equilibrium is investigated as local stability switches. Existence of global continuation of periodic solutions bifurcating from the interior equilibrium is discussed by using a global Hopf bifurcation theorem for functional differential equations. Numerical simulations are provided to show consistency with theoretical analysis.
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