Stochastic foraging arena interaction of modified Leslie-type with
correlated Brownian motions under regime switching
Abstract
In this paper we incorporate the white noise and Markovian switching
into the modified Leslie-type predator-prey model with foraging arena
scheme. Especially, the parametric conditions for the system to be
permanent or extinct are investigated. Inspired by
\cite{Dieu2016classification,hening2017stochastic}, we
also consider how the correlations between the Brownian motions affect
the population interactions. Numerical simulations are carried out to
substantiate the analytical results.