Global Dynamics of a Stage Structure Prey–Predator Model With Fear, Group Defense, and Antipredator Behavior

Abstract

This study proposes a 3-D stage-structured model, in which predator population is classified into immature and mature groups. The effect of mature predator's fear and the prey's antipredator behavior toward the juvenile predators are investigated. Furthermore, the effect of prey's collective defense in lowering the threat of predators is also examined. The investigation includes local stability analysis for existing steady-state solutions, revealing a number of global and local bifurcations such as homoclinic, transcritical, Hopf, and saddle-node bifurcations, as well as a codimension two Bogdanov–Takens bifurcation. We noticed that the tendency of prey to form groups causes the solutions to behave oscillatorily and that the level of fear eliminates these fluctuations and brings the system to a stable coexistence. The predator experiences a catastrophic fall when antipredator nature intensifies beyond a certain degree. The model also demonstrates bubbling phenomena in the maturation rate and the paradox of enrichment. To elucidate these bifurcations, we conduct biparametric analyses for various parameters, emphasizing their critical roles in predator survival and extinction. Numerical simulations and graphical illustrations validate our theoretical findings, demonstrating how fear, group defense, maturation rate, and counter attack behavior enrich the system dynamics.