Dynamical Behavior of Canada Lynx and Snowshoe Hare Population in Fluctuating Environment

The motivation of this work is to analyze the dynamical behavior of specialist predator Canada lynx preying on snowshoe hare. A stochastic non-autonomous one-prey one-predator system is formed with prey-refuge and quadratic harvesting in predator species. Firstly, the feasibility of our model has been obtained by proving the existence and uniqueness of a global positive solution. Next, sufficient conditions for prey-predator extinction, non-persistence, weakly persistence, and permanence have been demonstrated. Also, the global attractiveness of the model has been shown. All the outcomes are verified numerically and the effect of prey refuge is illustrated. Finally, the conclusion is given.