In the real world, the population systems are often subject to white noises and a system with such stochastic perturbations tends to be suitably modeled by stochastic differential equations. This paper is concerned wi...In the real world, the population systems are often subject to white noises and a system with such stochastic perturbations tends to be suitably modeled by stochastic differential equations. This paper is concerned with the dynamic behaviors of a delay stochastic competitive system. We first obtain the global existence of a unique positive solution of system. Later, we show that the solution of system will be stochastically ultimate boundedness. However, large noises may make the system extinct exponentially with probability one. Also, sufficient conditions for the global attractivity of system are established. FinMly, illustrated examples are given to show the effectiveness of the proposed criteria.展开更多
In this paper, a modified nonlinear dynamic inequality on time scales is used to study the boundedness of a class of nonlinear third-order dynamic equations on time scales. These theorems contain as special cases resu...In this paper, a modified nonlinear dynamic inequality on time scales is used to study the boundedness of a class of nonlinear third-order dynamic equations on time scales. These theorems contain as special cases results for dynamic differential equations, difference equations and q-difference equations.展开更多
基金Acknowledgments The authors thank the referees for their reports and many valuable comments and suggestions that greatly improved the presentation of this paper. The work is supported by the National Natural Science Foundation of China （No. 11261017）, the Key Laboratory of Biological Resources Protection and Utilization of Hubei Province （No. PKLHB1323） and the Key Project of Chinese Ministry of Education （No. 212111）.
文摘In the real world, the population systems are often subject to white noises and a system with such stochastic perturbations tends to be suitably modeled by stochastic differential equations. This paper is concerned with the dynamic behaviors of a delay stochastic competitive system. We first obtain the global existence of a unique positive solution of system. Later, we show that the solution of system will be stochastically ultimate boundedness. However, large noises may make the system extinct exponentially with probability one. Also, sufficient conditions for the global attractivity of system are established. FinMly, illustrated examples are given to show the effectiveness of the proposed criteria.
基金partially supported by the NSF of China(Grant.11271225)Program for Scientific Research Innovation Team in Colleges and Universities of Shandong Province
文摘In this paper, a modified nonlinear dynamic inequality on time scales is used to study the boundedness of a class of nonlinear third-order dynamic equations on time scales. These theorems contain as special cases results for dynamic differential equations, difference equations and q-difference equations.
