Stochastic bifurcation and density function analysis of a stochastic logistic equation with distributed delay and weak kernel.

Stochastic bifurcation theory plays an important role in stochastic dynamical systems, thus, in this paper, we mainly consider the stochastic bifurcation of a stochastic logistic model with distributed delay in the weak kernel case, where the birth rate of species is disturbed by white noise. In order to study the bifurcation of stochastic logistic system, we use the intrinsic growth rate of species as a bifurcation parameter. Firstly, we study the stochastic D-bifurcation and stochastic P-bifurcation for stochastic logistic model with distributed delay. Furthermore, by deriving the corresponding Fokker–Planck equation, we obtain the exact expression of the joint density function of the stochastic system near the positive equilibrium point. Finally, we give some conclusions. [ABSTRACT FROM AUTHOR]