Abstract
In this paper, we study a stochastic predator–prey model with distributed delay and general functional response. We transform the model with weak kernel case into an equivalent system through the linear chain technique. Since the diffusion matrix is degenerate, the uniform ellipticity condition does not hold. The Markov semigroup theory is used to derive the existence of a unique stable stationary distribution. We verify the densities of the distributions of the positive solutions can converge in L1 to an invariant density.
•Stochastic predator–prey model with distributed delay and general functional response is studied.•We transform the model with weak kernel case into an equivalent system.•The densities of the distributions of the solutions can be proved converge to an invariant density.