Abstract
On the basis of the cost of fear and the strength of refuge on prey
species, a stochastic competition models with impulsive effects be
formulated. First, by constructing the appropriate Lyapunov function,
the existences of a unique global positive solution for the equivalent
stochastic system and the stochastic system with impulse are proven.
Then, using Itô formula, the stochastic Lyapunov function and some
important inequalities, we obtained the sufficient conditions of
extinction, non-mean persistence, mean persistence, random persistence
and global attraction of system. Finally, through numerical simulation,
the impacts of the cost of fear and the strength of refuge, as well as
random and impulsive disturbances on predator population were
intuitively illustrated.