Abstract
In this article, a system of delay differential equations to represent the predator–prey dynamics with weak Allee effect in the growth of predator population is discussed. The delay parameter regarding the time lag corresponds to the predator gestation period. Mathematical features such as uniform persistence, permanence, stability, Hopf bifurcation at the interior equilibrium point of the system are analyzed and verified by numerical simulations. Bistability between different equilibrium points is properly discussed. The chaotic behaviors of the system are recognized through bifurcation diagram, Poincare section, and maximum Lyapunov exponent. By constructing a suitable Lyapunov functional for the time-delayed model, global asymptotic stability analysis of the positive equilibrium points has been performed separately. It can be observed that the Allee parameter $$\theta $$ can destabilize the non-delay system, whereas $$\theta $$ and the attack rate of predator can stabilize the time-delayed model and can control the chaotic oscillations through period-halving bifurcation. The optimal predator control policy with Allee parameter ( $$\theta $$ ) as the control parameter is also discussed.
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