The use of flocculants to collect/extract microorganisms is of great practical significance for the development of the application of microorganisms. In this paper, a high-dimensional nonlinear stochastic differential...The use of flocculants to collect/extract microorganisms is of great practical significance for the development of the application of microorganisms. In this paper, a high-dimensional nonlinear stochastic differential equation model is constructed to describe the continuous culture of microorganisms with multiple nutrients and the flocculation process of microorganisms. The study of the dynamics of this model can provide feasible control strategies for the collection/extraction of microorganisms. The main theoretical results are sufficient conditions for the permanence and extinction of the stochastic differential equation model, which are also extensions of some results in the existing literatures. In addition, through numerical simulations, we vividly demonstrate the statistical characteristics of the stochastic differential equation model.展开更多
A stochastic susceptible-infective-recovered(SIR)epidemic model with jumps was considered.The contributions of this paper are as follows.(1) The stochastic differential equation(SDE)associated with the model has a uni...A stochastic susceptible-infective-recovered(SIR)epidemic model with jumps was considered.The contributions of this paper are as follows.(1) The stochastic differential equation(SDE)associated with the model has a unique global positive solution;(2) the results reveal that the solution of this epidemic model will be stochastically ultimately bounded,and the non-linear SDE admits a unique stationary distribution under certain parametric conditions;(3) the coefficients play an important role in the extinction of the diseases.展开更多
A stochastic susceptible-infective-recovered-susceptible( SIRS) model with non-linear incidence and Levy jumps was considered. Under certain conditions, the SIRS had a global positive solution. The stochastically ulti...A stochastic susceptible-infective-recovered-susceptible( SIRS) model with non-linear incidence and Levy jumps was considered. Under certain conditions, the SIRS had a global positive solution. The stochastically ultimate boundedness of the solution of the model was obtained by using the method of Lyapunov function and the generalized Ito's formula. At last,asymptotic behaviors of the solution were discussed according to the value of R0. If R0< 1,the solution of the model oscillates around a steady state, which is the diseases free equilibrium of the corresponding deterministic model,and if R0> 1,it fluctuates around the endemic equilibrium of the deterministic model.展开更多
In this paper,we investigate a two-dimensional avian influenza model with Allee effect and stochasticity.We first show that a unique global positive solution always exists to the stochastic system for any positive ini...In this paper,we investigate a two-dimensional avian influenza model with Allee effect and stochasticity.We first show that a unique global positive solution always exists to the stochastic system for any positive initial value.Then,under certain conditions,this solution is proved to be stochastically ultimately bounded.Furthermore,by constructing a suitable Lyapunov function,we obtain sufficient conditions for the existence of stationary distribution with ergodicity.The conditions for the extinction of infected avian population are also analytically studied.These theoretical results are conformed by computational simulations.We numerically show that the environmental noise can bring different dynamical outcomes to the stochastic model.By scanning different noise intensities,we observe that large noise can cause extinction of infected avian population,which suggests the repression of noise on the spread of avian virus.展开更多
This paper investigates a stochastic Holling II predator-prey model with Levy jumps and habit complexity.It is first proved that the established model admits a unique global positive solution by employing the Lyapunov...This paper investigates a stochastic Holling II predator-prey model with Levy jumps and habit complexity.It is first proved that the established model admits a unique global positive solution by employing the Lyapunov technique,and the stochastic ultimate boundedness of this positive solution is also obtained.Sufficient conditions are established for the extinction and persistence of this solution.Moreover,some numerical simulations are carried out to support the obtained results.展开更多
In this paper,stochastic properties of solution for a chemostat model with a distributed delay and random disturbance are studied,and we use distribution delay to simulate the delay in nutrient conversion.By the linea...In this paper,stochastic properties of solution for a chemostat model with a distributed delay and random disturbance are studied,and we use distribution delay to simulate the delay in nutrient conversion.By the linear chain technique,we transform the stochastic chemostat model with weak kernel into an equivalent degenerate system which contains three equations.First,we state that this model has a unique global positive solution for any initial value,which is helpful to explore its stochastic properties.Furthermore,we prove the stochastic ultimate boundness of the solution of system.Then sufficient conditions for solution of the system tending toward the boundary equilibrium point at exponential rate are established,which means the microorganism will be extinct.Moreover,we also obtain some sufficient conditions for ergodicity of solution of this system by constructing some suitable stochastic Lyapunov functions.Finally,we provide some numerical examples to illustrate theoretical results,and some conclusions and analysis are given.展开更多
A stochastic two-species Schoener's competitive model is proposed and investigated. Sufficient conditions for the existence of global positive solutions, boundedness~ uniform continuity, global attractivity stochasti...A stochastic two-species Schoener's competitive model is proposed and investigated. Sufficient conditions for the existence of global positive solutions, boundedness~ uniform continuity, global attractivity stochastic permanence and extinction are obtained. More- over, the upper-growth rate and the average in time of the sample paths of solutions are also estimated. Finally, some figures are introduced to illustrate the main results.展开更多
基金the National Natural Science Foundation of China (Grant No. 11971055)the Beijing Natural Science Foundation, China (Grant No. 1202019)。
文摘The use of flocculants to collect/extract microorganisms is of great practical significance for the development of the application of microorganisms. In this paper, a high-dimensional nonlinear stochastic differential equation model is constructed to describe the continuous culture of microorganisms with multiple nutrients and the flocculation process of microorganisms. The study of the dynamics of this model can provide feasible control strategies for the collection/extraction of microorganisms. The main theoretical results are sufficient conditions for the permanence and extinction of the stochastic differential equation model, which are also extensions of some results in the existing literatures. In addition, through numerical simulations, we vividly demonstrate the statistical characteristics of the stochastic differential equation model.
基金Natural Science Foundation of Hunan University of Technology,China(No.2012HZX08)the Special Foundation of National Independent Innovation Demonstration Area Construction of Zhuzhou(Applied Basic Research),China
文摘A stochastic susceptible-infective-recovered(SIR)epidemic model with jumps was considered.The contributions of this paper are as follows.(1) The stochastic differential equation(SDE)associated with the model has a unique global positive solution;(2) the results reveal that the solution of this epidemic model will be stochastically ultimately bounded,and the non-linear SDE admits a unique stationary distribution under certain parametric conditions;(3) the coefficients play an important role in the extinction of the diseases.
基金National Natural Science Foundations of China(No.11071259,No.11371374)Research Fund for the Doctoral Program of Higher Education of China(No.20110162110060)
文摘A stochastic susceptible-infective-recovered-susceptible( SIRS) model with non-linear incidence and Levy jumps was considered. Under certain conditions, the SIRS had a global positive solution. The stochastically ultimate boundedness of the solution of the model was obtained by using the method of Lyapunov function and the generalized Ito's formula. At last,asymptotic behaviors of the solution were discussed according to the value of R0. If R0< 1,the solution of the model oscillates around a steady state, which is the diseases free equilibrium of the corresponding deterministic model,and if R0> 1,it fluctuates around the endemic equilibrium of the deterministic model.
基金This study is supported by the National Key Research and Development Program of China(2018YFA0801103)the National Natural Science Foundation of China(Grant No.12071330 to Ling Yang,Grant No.11701405 to Jie Yan).
文摘In this paper,we investigate a two-dimensional avian influenza model with Allee effect and stochasticity.We first show that a unique global positive solution always exists to the stochastic system for any positive initial value.Then,under certain conditions,this solution is proved to be stochastically ultimately bounded.Furthermore,by constructing a suitable Lyapunov function,we obtain sufficient conditions for the existence of stationary distribution with ergodicity.The conditions for the extinction of infected avian population are also analytically studied.These theoretical results are conformed by computational simulations.We numerically show that the environmental noise can bring different dynamical outcomes to the stochastic model.By scanning different noise intensities,we observe that large noise can cause extinction of infected avian population,which suggests the repression of noise on the spread of avian virus.
基金supported by the National Natural Science Foundation of China(Nos.11901398,11671149,11871225 and 11771102)Guangdong Basic and Applied Basic Research Foundation(No.2019A1515011350)the Fundamental Research Funds for the Central Universities(No.2018MS58).
文摘This paper investigates a stochastic Holling II predator-prey model with Levy jumps and habit complexity.It is first proved that the established model admits a unique global positive solution by employing the Lyapunov technique,and the stochastic ultimate boundedness of this positive solution is also obtained.Sufficient conditions are established for the extinction and persistence of this solution.Moreover,some numerical simulations are carried out to support the obtained results.
基金supported by the National Natural Science Foundation of China(Nos.11771044 and 11871007).
文摘In this paper,stochastic properties of solution for a chemostat model with a distributed delay and random disturbance are studied,and we use distribution delay to simulate the delay in nutrient conversion.By the linear chain technique,we transform the stochastic chemostat model with weak kernel into an equivalent degenerate system which contains three equations.First,we state that this model has a unique global positive solution for any initial value,which is helpful to explore its stochastic properties.Furthermore,we prove the stochastic ultimate boundness of the solution of system.Then sufficient conditions for solution of the system tending toward the boundary equilibrium point at exponential rate are established,which means the microorganism will be extinct.Moreover,we also obtain some sufficient conditions for ergodicity of solution of this system by constructing some suitable stochastic Lyapunov functions.Finally,we provide some numerical examples to illustrate theoretical results,and some conclusions and analysis are given.
基金This work was supported by the National Natural Science Foundation of P. R. China (No. 11171081, 11171056), the Natural Scientific Research Innovation Foundation in Harbin Institute of Technology (No. HIT.NSRIF.2011094), and the Scientific Research Foundation of Harbin Institute of Technology at Weihai (No. HIT (WH) ZB201103).
文摘A stochastic two-species Schoener's competitive model is proposed and investigated. Sufficient conditions for the existence of global positive solutions, boundedness~ uniform continuity, global attractivity stochastic permanence and extinction are obtained. More- over, the upper-growth rate and the average in time of the sample paths of solutions are also estimated. Finally, some figures are introduced to illustrate the main results.