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

Since the stochastic bifurcation theory is still in its infancy,we try to analyze some stochastic bifurcation phenomenon from a simple mathematical model.Thus,this paper mainly focuses on studying the stochastic bifurcation of a stochastic logistic model with distributed delay in the strong kernel case,which is affected by noise.Therefore,we use the intrinsic growth rate as a bifurcation parameter.First,we study the stochastic D-bifurcation and stochastic P-bifurcation for stochastic logistic model.Furthermore,by deriving the corresponding Fokker-Planck equation,we obtain the expression of the joint density function of the stochastic logistic system near the positive equilibrium point.Finally,some conclusions are given.