Subsurface Flow and Transport: A Stochastic Approach

In this paper, we explore an impulsive stochastic infected predator-prey system with Levy jumps and delays. The main aim of this paper is to investigate the effects of time delays and impulse stochastic interference on dynamics of the predator-prey model. First, we prove some properties of the subsystem of the system. Second, in view of comparison theorem and limit superior theory, we obtain the sufficient conditions for the extinction of this system. Furthermore, persistence in mean of the system is also investigated by using the theory of impulsive stochastic differential equations (ISDE) and delay differential equations (DDE). Finally, we carry out some simulations to verify our main results and explain the biological implications.

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Extinction and Persistence in Mean of a Novel Delay Impulsive Stochastic Infected Predator-Prey System with Jumps

Dynamics of a stochastic one-prey two-predator model with Lévy jumps

This article explores a stochastic ratio-dependent predator-prey model with regime-switching. We testify that the model admits a unique stationary distribution, and demonstrate that the transition probability of the solution of the model converges to the stationary distribution in exponent rate. We also discuss the biological implications of the results by aid of some numerical simulations.

Stationary distribution of a stochastic ratio-dependent predator-prey system with regime-switching

In this paper, we employ the multilevel Monte Carlo finite element method to solve the stochastic Cahn-Hilliard-Cook equation. The Ciarlet-Raviart mixed finite element method is applied to solve the fourth-order equation. In order to estimate the mild solution, we use finite elements for space discretization and the semi-implicit Euler-Maruyama method in time. For the stochastic scheme, we use the multilevel method to decrease the computational cost (compared to the Monte Carlo method). We implement the method to solve three specific numerical examples (both two- and three dimensional) and study the effect of different noise measures.

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A multilevel Monte Carlo finite element method for the stochastic Cahn-Hilliard-Cook equation.

Conforming finite element methods for the stochastic Cahn–Hilliard–Cook equation

Weak-Galerkin finite element methods for a second-order elliptic variational inequality

Reconstruction for Sturm–Liouville operators with frozen argument for irrational cases

Analysis of a stochastic ratio-dependent predator–prey model driven by Lévy noise

The weak Galerkin form of the finite element method, requiring only C0 basis function, is applied to the biharmonic equation. The computational procedure is thoroughly considered. Local orthogonal bases on triangulations are constructed using various sets of interpolation points with the Gram-Schmidt or Levenberg-Marquardt methods. Comparison and high-precision computations are carried out, and convergence rates are provided up to degree 11 for L2, 10 for H1, and 9 for H2, suggesting that the algorithm is useful for a variety of computations.

Wenju Zhao

Papers

Conforming finite element methods for the stochastic Cahn–Hilliard–Cook equation

Weak-Galerkin finite element methods for a second-order elliptic variational inequality

Reconstruction for Sturm–Liouville operators with frozen argument for irrational cases

Analysis of a stochastic ratio-dependent predator–prey model driven by Lévy noise

High-precision computation of the weak Galerkin methods for the fourth-order problem