Hopf Bifurcation in an Age‐Structured Predator–Prey System With Beddington–DeAngelis Functional Response and Double Time Delays

ABSTRACT This work is concerned with the existence of Hopf bifurcations in an age‐structured predator–prey model involved with a reaction time delay and a maturation period . It is assumed that the predator fertility function is represented as a piecewise function dependent on the maturation period . First, we reformulate the original system as a nondensely defined abstract Cauchy problem and analyze the existence and uniqueness of equilibria, the associated linear system and the characteristic equation of the reformulated problem. Next, in the case of and change independently, we observe that the system exhibits a series of S‐stepped‐like curves and Hopf bifurcation occur at the positive equilibrium. Then, under the condition , we treat the delay as a bifurcation parameter and examine the occurrence of Hopf bifurcation at the positive equilibrium by applying the integrated semigroup theory and the Hopf bifurcation theorem. Finally, numerical simulations are conducted to validate the theoretical findings, demonstrating the reliability and applicability of the results.