Mathematical Insights into Cannibalistic Predators: A Dynamical System Approach

Cannibalistic Predator-Prey Model

Résumé

Cannibalism, the act of consuming individuals of the same species, is a familiar phenomenon in many natural population. While it may serve as a survival strategy under conditions of resource scarcity, its occurrence tends to decrease with the increased availability of food sources. In this current study, we employ the theory of dynamical system to investigate the dynamics of a cannibalistic predator-prey model when the cannibalism is a decreasing function of availability of food sources. A detailed mathematical analysis is conducted to examine the permanence, stability and various bifurcation that occurring in the system. The study reveals various bifurcations such as, transcritical and Hopf bifurcation. From the system analysis, treating cannibalistic parameter and growth rate of predator are control parameters to study the dynamical analysis of the system and rest are treated as fixed parameters. This investigation founds the regions that of coexistence of the species which is important for biological conservation in the environment. Finally, numerical simulations are carried out to substantiate the analytical investigations.