Dynamics of a delay-induced prey–predator system with interaction between immature prey and predators

Abstract

In biological pest control systems, several pests (including insects, mites, weeds, etc.) are controlled by biocontrol agents that rely primarily on predation. Following this biocontrol management ecology, we have created a three-tier prey–predator model with prey phase structure and predator gestation delay. Several studies have demonstrated that predators with Holling type-II functional responses sometimes consume immature prey. A study of the well-posedness and local bifurcation (such as saddle-node and transcritical) near the trivial and planer equilibrium points is carried out. Without any time lag, the prey development coefficient has a stabilizing impact, while increasing attack rate accelerates instability. Energy transformation rate and handling time are shown to cause multiple stability switches in the system. Numerical results demonstrate time delay is the key destabilizer that destroys stability. Our model can replicate more realistic events by including time-dependent factors and exploring the dynamic behavior of nonautonomous systems. In the presence of time delay, sufficient conditions of permanence and global attractivity of the nonautonomous system are derived. Finally, MATLAB simulations are performed to validate the analytical findings.