In this paper we study the global dynamics of stochastic predator-prey models
with non constant mortality rate and Holling type II response. Concretely,
we establish sufficient conditions for the extinction and persistence in the
mean of autonomous stochastic model and obtain a critical value between
them. Then by constructing appropriate Lyapunov functions, we prove that
there is a nontrivial positive periodic solution to the non-autonomous
stochastic model. Finally, numerical examples are introduced to illustrate
the results developed.
AbstractIn this paper, we consider a nonautonomous predator–prey model with Holling type II schemes and a prey refuge. By applying the comparison theorem of differential equations and constructing a suitable Lyapunov function, sufficient conditions that guarantee the permanence and global stability of the system are obtained. By applying the oscillation theory and the comparison theorem of differential equations, a set of sufficient conditions that guarantee the extinction of the predator of the system is obtained.
Qualitative analysis of a predator–prey model with Holling type II functional response incorporating a prey refuge