This paper aims at the detailed numerical analysis of a cyclic three species predator–prey model where the prey consumes only a part of the super-predator population. Such a model exists only when the prey acts as an omnivore. Here, we have investigated the dynamical behaviour of the prey, middle predator and super-predator. All the possible equilibrium points of the model are computed and the existence and stability condition of the equilibrium states are determined. The phase portraits are generated for different sets of parameter values. The long term behaviour of the system is investigated by studying the bifurcation structure and nature of the attractors, thereby identifying the domain of chaos, as each of the control parameter is varied independently. Finally, we show that a transition from chaotic domain to escape or vice-versa of the predator in a small region of the parameter plane leads to a fractal structure.
Volume 95, 2021
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