By constructing a suitable Lyapunov function,sufficient conditions which ensure the global asymptotical stability of the positive equilibrium and boundary equilibrium of an obligate Lotka-Volterra mutualism model are ...By constructing a suitable Lyapunov function,sufficient conditions which ensure the global asymptotical stability of the positive equilibrium and boundary equilibrium of an obligate Lotka-Volterra mutualism model are obtained,respectively.It is shown that the conditions which ensure the local stability of the nonnegative equilibria is enough to ensure their global asymptotical stability.Our result supplements and complements some known result.展开更多
In this paper, a Lotka-Volterra cooperation system with single feedback control is proposed and studied. We investigate the local stability and the global stability of the system. Our study shows that with suitable re...In this paper, a Lotka-Volterra cooperation system with single feedback control is proposed and studied. We investigate the local stability and the global stability of the system. Our study shows that with suitable restriction on the coefficients of the feedback control variable, the system can still remain globally stable or become extinct, which shows that the feedback control variable plays a very important role in the dynamics behaviors of the system.展开更多
A two species discrete commensalism system is proposed and studied. By the Jury＇s conditions for the stability of second order discrete system, the local stability property of positive equilibrium is investigated; af...A two species discrete commensalism system is proposed and studied. By the Jury＇s conditions for the stability of second order discrete system, the local stability property of positive equilibrium is investigated; after that, sufficient conditions which ensure the global asymptotic stability of the interior equilibrium are obtained. An example together with its numeric simulation is given to illustrate the feasibility of the main result.展开更多
An autonomous stage-structured ratio-dependent cooperative system, which was proposed by Muhammadhaji, Teng and Abdurahman, is revisited in this paper. By introducing a new lemma and using the iterative method, a set ...An autonomous stage-structured ratio-dependent cooperative system, which was proposed by Muhammadhaji, Teng and Abdurahman, is revisited in this paper. By introducing a new lemma and using the iterative method, a set of sufficient conditions which guarantee the global attractivity of the positive equilibrium is obtained. It is shown that the conditions which guarantee the permanence of the system are enough to ensure the global attractivity of the system. Our result not only complements but also supplements one of the main results of Muhammadhaji, Teng and Abdurahman （Permanence and extinction analysis for a delayed ratio-dependent cooperative system with stage structure, Afr. Mat.（2013）DOI 10.1007/s13370-013-0162-6）.展开更多
基金supported by the Natural Science Foundation of Pujian Province(2013J01011,2013J01010)the Foundation of Fujian Edication Bureau(JA13361)
文摘By constructing a suitable Lyapunov function,sufficient conditions which ensure the global asymptotical stability of the positive equilibrium and boundary equilibrium of an obligate Lotka-Volterra mutualism model are obtained,respectively.It is shown that the conditions which ensure the local stability of the nonnegative equilibria is enough to ensure their global asymptotical stability.Our result supplements and complements some known result.
基金supported by the Natural Science Foundation of Fujian Province(2013J01011,2013J01010)
文摘In this paper, a Lotka-Volterra cooperation system with single feedback control is proposed and studied. We investigate the local stability and the global stability of the system. Our study shows that with suitable restriction on the coefficients of the feedback control variable, the system can still remain globally stable or become extinct, which shows that the feedback control variable plays a very important role in the dynamics behaviors of the system.
基金supported by the Natural Science Foundation of Fujian Province(2015J01012,2015J01019)
文摘A two species discrete commensalism system is proposed and studied. By the Jury＇s conditions for the stability of second order discrete system, the local stability property of positive equilibrium is investigated; after that, sufficient conditions which ensure the global asymptotic stability of the interior equilibrium are obtained. An example together with its numeric simulation is given to illustrate the feasibility of the main result.
基金supported by the Natural Science Foundation of Fujian Province(2013J01011,2013J01010)the Foundation of Fujian Edication Bureau(JA13361)
文摘An autonomous stage-structured ratio-dependent cooperative system, which was proposed by Muhammadhaji, Teng and Abdurahman, is revisited in this paper. By introducing a new lemma and using the iterative method, a set of sufficient conditions which guarantee the global attractivity of the positive equilibrium is obtained. It is shown that the conditions which guarantee the permanence of the system are enough to ensure the global attractivity of the system. Our result not only complements but also supplements one of the main results of Muhammadhaji, Teng and Abdurahman （Permanence and extinction analysis for a delayed ratio-dependent cooperative system with stage structure, Afr. Mat.（2013）DOI 10.1007/s13370-013-0162-6）.
