The environmental effect on dynamics of the competition model with herd behavior

Abstract

In this paper, the competition model with herd behavior and the Allee effect, which dynamics is described by the two-dimensional system of stochastic differential equations, is considered. We verify that the environmental noise included in the model provides a solution that is positive, global and bounded. Conditions under which the system is stable in some sense are presented. Finally, as an illustration, we apply our mathematical results for the prediction of time for which populations of the Asiatic black bear (Ursus thibetanus) and wild boar (Sus scrofa) in the Mount Jiri National Park, need to reach their equilibrium state.