Numerical exploration of the parameter plane in a discrete predator–prey model

• A new discrete model for predator–prey interactions is proposed and its ecological relevance is discussed.
• The general pattern of bifurcations and the changes in the nature of the attractors studied by varying the control parameters.
• The domain of chaos in the parameter plane identified using a dimensional analysis.

We propose a variant of the discrete Lotka–Volterra model for predator–prey interactions. A detailed stability and numerical analysis of the model are presented to explore the long time behaviour as each of the control parameter is varied independently. We show how the condition for survival of the predator depends on the natural death rate of predator and the efficiency of predation. The model is found to support different dynamical regimes asymptotically including predator extinction, stable fixed point and limit cycle attractors for co-existence of predator and prey and more complex dynamics involving chaotic attractors. We are able to locate exactly the domain of chaos in the parameter plane using a dimensional analysis.