Deterministic and stochastic analysis of a two-prey-one-predator system with fear effect and switching behaviour in predation

In this article, we have analysed a two-prey-one-predator system in which predator feeds on the more abundant prey species (switching in predation) and also the reproduction of both prey species is greatly reduced by the presence of predator (fear affect). The goal of this work is to investigate the dynamical characteristics of the system in both deterministic and stochastic environments. Well-posedness of the deterministic system has been justified by analysing the basic dynamical properties of that system. Stability conditions at various feasible equilibrium points are derived in terms of model parameters. The impact of parametric fluctuation has also been investigated on the model dynamics by using local bifurcation analysis. We also have studied the proposed model in a fluctuating environment by considering death rate of each species as stochastic parameter. Our mathematical findings have been justified and illustrated through numerical simulation.

Automated summary

In this article, a two-prey-one-predator system is analyzed, with the predator feeding on the more abundant prey species and the reproduction of both prey species greatly reduced by the presence of the predator. The goal is to investigate the dynamical characteristics of the system in both deterministic and stochastic environments by analyzing the basic properties of the deterministic system and deriving stability conditions at various equilibrium points. The impact of parameter fluctuations on the model dynamics is studied using local bifurcation analysis, and the proposed model is also studied in a fluctuating environment by considering stochastic death rates for each species. The mathematical findings are justified and illustrated through numerical simulations.