Abstract
This paper aims to investigate how the external random noise affects the dynamics of the predator-prey model with a modified Leslie and foraging arena scheme. The autonomous and non-autonomous systems are both considered. First, some asymptotic behaviors of two species are explored including the threshold point. Then, the existence of an invariant density is deduced, based on the theory elaborated in Pike and Luglato (1987). Moreover, the famous LaSalle-type theorem is applied to investigate weak extinction, which requires weaker parametric restrictions. A numerical study is conducted to illustrate our theory.
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