Deterministic and stochastic analysis of a predator-prey model with Allee effect and herd behaviour

摘要

This paper aims to study the dynamics of a predator-prey model, where both prey and predator show herd behaviour. Due to this behaviour, predator-prey interaction occurs only at the outer edge of herds formed by the populations. Positivity and boundedness of the system are discussed. A criteria for the extinction of prey is established. A steady-state analysis has been performed. Some criteria for Hopf bifurcation are derived. The stochastic version of the model is formulated to take into account the effect of fluctuating environment. A criterion of asymptotic mean square stability of this model is derived. Numerical simulations are carried out to validate our analytical findings. Implications of our analytical and numerical findings are discussed critically.