Dynamical Complexity in a Class of Novel Discrete-Time Predator-Prey Interaction With Cannibalism

Cannibalism is ubiquitous in natural communities and has the tendency to change the functional connection among prey-predator interactions. Keeping in view the inclusion of prey cannibalism, a novel discrete nonlinear predator-prey model is proposed. Asymptotic stability is carried out around biologically feasible equilibria of proposed model. Center manifold theorem and bifurcation theory of normal form ensure the existence of bifurcation in the system. Our study reveals that periodic outbreaks may result due to incorporation of cannibalism in prey population and this periodic outbreak is limited to prey population only without leaving an effect on predation. In order to control these periodic oscillations in prey population density and other bifurcating and fluctuating behavior of the system, various chaos control strategies are implemented. Ultimately, some extensive numerical simulations are elaborated to demonstrate the effectiveness of our acquired analytical and theoretical results.