In this paper, a delayed ratio-dependent Holling-III predator-prey system with stagestructured and impulsive stocking on prey and continuous harvesting on predator is considered. The authors obtain sufficient conditio...In this paper, a delayed ratio-dependent Holling-III predator-prey system with stagestructured and impulsive stocking on prey and continuous harvesting on predator is considered. The authors obtain sufficient conditions of the global attractivity of predator-extinction periodic solution and the permanence of the system. These＇ results show that the behavior of impulsive stocking on prey plays an important role for the permanence of the system. The authors also prove that all solutions of the system are uniformly ultimately bounded. The results show that the biological resource management is effective and reliable. Key words Globally attractivity, impulsive effect, permanence, ratio-dependent, stage-structured.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
In this paper, we investigate the existence, stability and global attractivity of T-periodic solutions for a class of quasilinear parabolic equations under Robin boundary conditions. We obtain that periodic solutions ...In this paper, we investigate the existence, stability and global attractivity of T-periodic solutions for a class of quasilinear parabolic equations under Robin boundary conditions. We obtain that periodic solutions exist if the inter-specific competition rates are weak. The numerical simulations are also presented to illustrate our result.展开更多
文摘In this paper, a delayed ratio-dependent Holling-III predator-prey system with stagestructured and impulsive stocking on prey and continuous harvesting on predator is considered. The authors obtain sufficient conditions of the global attractivity of predator-extinction periodic solution and the permanence of the system. These＇ results show that the behavior of impulsive stocking on prey plays an important role for the permanence of the system. The authors also prove that all solutions of the system are uniformly ultimately bounded. The results show that the biological resource management is effective and reliable. Key words Globally attractivity, impulsive effect, permanence, ratio-dependent, stage-structured.
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.
文摘In this paper, we investigate the existence, stability and global attractivity of T-periodic solutions for a class of quasilinear parabolic equations under Robin boundary conditions. We obtain that periodic solutions exist if the inter-specific competition rates are weak. The numerical simulations are also presented to illustrate our result.
