Dynamic analysis of a Leslie-Gower model with additive Allee effect on the prey population and predator harvesting including stochastic effect on each population

Abstract

In this study, we proposed a Leslie-Gower prey-predator model, whose dynamics includes a constant effort harvesting rate in predators and an additive Allee impact on prey. A system of stochastic differential equations is also used to study its behaviour, with the assumption that each population's exposure to environmental unpredictability is represented by noise terms. This kind of randomness is considerably more reasonable and realistic in the proposed paradigm. Due to the paucity of studies on the dynamics of this kind of model, this investigation is being believed to be a way to advance the subject of literature. First, we establish the system's positivity and boundlessness. Next, we look into the dynamics of every one of the stable states, the form of the positive equilibrium point, and the continued existence of every species in the system.It is established that the equilibrium levels of prey and predator are impacted by the Allee effect parameter as well as the impact of harvesting. The positive steady state point's global stability criterion is derived. By selecting the Allee effect and harvesting effort as the bifurcation parameters, it has been established that a Hopf bifurcation exists close to the interior steady state.This study is novel since it incorporates various ecological factors into a single model, potentially opening up new perspectives on predator-prey relationships. To support the mathematical conclusions, rigorous numerical visualisations of the key parameters are provided below using specific hypothetical data. In conclusion, we may state that our model is a project that aims to preserve the ecological equilibrium of the natural world.

Keywords

• leslie-gower scheme
• allee effect
• harvesting
• stochastic effect
• stability
• hopf bifurcation