Complex Dynamical Behavior of a Three Species Prey-Predator System with Nonlinear Harvesting

In this manuscript, we consider an extended version of the prey-predator system with nonlinear harvesting [Gupta et al., 2015] by introducing a top predator (omnivore) which feeds on more than one trophic levels. Consideration of third species as omnivore makes the system a food web of three populations. We have guaranteed positivity as well as the boundedness of solutions of the proposed system. We observed that the presence of third species complicates the dynamical behavior of the system. It is also observed that multiple positive steady states exist for the proposed system which makes the problem more interesting compared to the similar models studied previously. Sotomayor's theorem is being utilized to study the saddle-node bifurcation. The persistence conditions are discussed for the proposed model. The local existence of periodic solution through Hopf bifurcations is also guaranteed numerically. It is observed that the proposed model is capable to exhibit more complicated dynamics in the form of chaos in both the cases when there are unique and multiple coexisting steady states. Bifurcation diagrams and Lyapunov exponents have been drawn to ensure the existence of chaotic dynamics of the system.