Delay-Induced Dynamics in a Stage-Structured Food Chain Model

Abstract

An investigation is performed into a non-linear mathematical model with a stage structure for a predator. The model shows that predators may be classified as both immature or mature. A time delay represents the age of adulthood, and immature predators are no longer capable of attack prey. Standards for the system's boundedness are installed. The presence of the equilibrium point and the stability of model are analyzed using the concepts of ordinary differential equations (ODEs). Additionally, the factors affecting gadget persistence are determined. A bifurcation analysis is done to assess the system's stability and instability in the presence of delay. The system's global stability is likewise verified graphically. Numerical simulations reveal that to govern the middle predator (pest) in the prey (plant), changes to each maturation delay and maturation fee are necessary.