Analysis of cannibalistic predator-prey model with defense and harvesting

The reciprocal link between living beings and their environment creates an ecosystem. There is interaction between two or more species in an ecosystem, particularly prey and predators. Predators frequently engage in cannibalism in addition to prey consumption. This study presents a predator-prey model in a three-level food chain by considering the effects of prey defense, predator cannibalism, and harvesting. The type IV Holling’s response function is used to demonstrate prey defense against predator. There are three populations in the model, namely the prey population, the middle predator population and the top predator population. This study demonstrates the solution’s limits of the model while also investigating the stability of the equilibrium point. Four equilibrium points were determined which two of them have been shown to be conditionally asymptotically stable, i.e. the equilibrium point representing the extinction of the three populations and the equilibrium point representing the extinction of middle and top predators. Through phase plane simulation with the specified parameter values, the stability of two more equilibrium points, i.e. the equilibrium point of extinction for top predator and the equilibrium point of coexistence, is demonstrated to be asymptotically stable. The study results also suggest that the obtained solution has a limit cycle. Furthermore, numerical simulations reveal that prey, middle predator, and top predator populations all exhibit the same increasing and decreasing trend.