Existence and persistence of positive solution for a stochastic turbidostat model

Developing a 3D stochastic discrete fracture network model for hydraulic analyses

Fluid flow in jointed rock mass with impermeable matrix is often controlled by joint properties, including aperture, orientation, spacing, persistence and etc. On the other hand, since the rock mass is made of heterogeneous and anisotropic natural materials, geometric properties of joints may have dispersed values. One of the most powerful methods for simulation of stochastic nature of geometri...

Asymptotic properties of a stochastic Gilpin-Ayala model under regime switching

In this paper, we consider a stochastic Gilpin-Ayala population model with Markovian switching and white noise. All parameters are influenced by stochastic perturbations. We analyze the existence of global positive solution, asymptotic stability in probability, pth moment exponential stability, extinction, weak persistence, stochastic permanence and stationary distribution of the model, which g...

Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion

The threshold behavior and periodic solution of stochastic SIR epidemic model with saturated incidence

In this article, we investigate degenerate stochastic SIR epidemic model with saturated incidence. For the constant coefficients case, we achieve a threshold which determines the extinction and persistence of the epidemic by utilizing Markov semigroup theory. Furthermore, we conclude that environmental white noise plays a positive effect in the control of infectious disease in some sense compar...

Dynamics of a stochastic non-autonomous predator-prey system with Beddington-DeAngelis functional response

A stochastic non-autonomous predator-prey system with Beddington-DeAngelis functional response is proposed, the existence of a global positive solution and stochastically ultimate boundedness are derived. Sufficient conditions for extinction, non-persistence in the mean, weak persistence in the mean and strong persistence in the mean are established. The global attractiveness of the solution is...