Abstract
The article is intended to study the Hopf−Zero bifurcation of a novel age-dependent predator−prey system with Monod−Haldane functional response comprising strong Allee effect. Here in this system the predators fertility function f(x) is regarded as a piecewise function with respect to their maturation period τ. The system is interpreted as a non-densely defined abstract Cauchy problem, and the condition of the existence and uniqueness of the non-negative steady state for a coupled dynamic system both a partial differential equation and an ordinary differential equation is yielded. Via employing the center manifold theorem and normal form theory for semilinear equations with non-dense domain, we discover much richer fresh dynamical behavior in an age-dependent predator−prey system than the existing ones.
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