Bifurcation analysis of a predator–prey model involving age structure, intraspecific competition, Michaelis–Menten type harvesting, and memory effect

The complexity of the dynamical behaviors of interaction between prey and its predator is studied. The prey and predator relationship involves the age structure and intraspecific competition on predators and the nonlinear harvesting of prey following the Michaelis–Menten type term. Some biological validities are shown for the constructed model such as the existence and uniqueness as well as the non-negativity and boundedness of solutions. Three equilibrium points, namely the origin, axial, and interior points, are found including their global dynamics by employing the Lyapunov function along with the generalized Lassale invariant principle. The changes in dynamical behaviors driven by the harvesting and the memory effect are exhibited, including transcritical, saddle-node, backward, and Hopf bifurcations. The appearance of these interesting phenomena is strengthened by giving numerical simulations consisting of bifurcation diagrams, phase portraits, and their time series