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
Traditional May type cooperative model incorporating Michaelis-Menten type harvesting is proposed and studied in this paper. Sufficient conditions which ensure the extinction of the first species and the existence of ...Traditional May type cooperative model incorporating Michaelis-Menten type harvesting is proposed and studied in this paper. Sufficient conditions which ensure the extinction of the first species and the existence of a unique globally attractive positive equilibrium are obtained, respectively. Numeric simulations are carried out to show the feasibility of the main results.展开更多
In this paper, we consider a modified Leslie-Clower predator prey model with Holling- type II schemes and mutual interference. By applying the comparison theorem of the differential equation and constructing a suitabl...In this paper, we consider a modified Leslie-Clower predator prey model with Holling- type II schemes and mutual interference. By applying the comparison theorem of the differential equation and constructing a suitable Lyapunov function, sufficient conditions which guarantee the permanence and existence of a unique globally attractive positive almost periodic solution of the system are obtained. Our results not only supplement but also improve some existing ones.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
We revisit the stability property of an ecological system consisting of a predator and stage structure prey which was proposed by Raid Kamel Naji and Salam Jasim Majeed. By constructing some suitable Lyapunov function...We revisit the stability property of an ecological system consisting of a predator and stage structure prey which was proposed by Raid Kamel Naji and Salam Jasim Majeed. By constructing some suitable Lyapunov function and applying the differential inequality theory, we show that the conditions which ensure the local stability of the vanishing point are enough to ensure its global stability. Our result supplements and complements some known results.展开更多
In this paper, the almost periodic predator-prey-mutualist model with Holling type II functional response is discussed. A set of sufficient condi- tions which guarantee the uniform persistence and the global attractiv...In this paper, the almost periodic predator-prey-mutualist model with Holling type II functional response is discussed. A set of sufficient condi- tions which guarantee the uniform persistence and the global attractivity of the system are obtained. For the almost periodic case, by constructing a suit- able Lyapunov function, sufficient conditions which guarantee the existence of a unique globally attractive positive almost periodic solution of the system are obtained. An example together with its numerical simulations shows the feasibility of the main results.展开更多
A nonautonomous ratio-dependent Leslie system incorporating a prey refuge is studied in this paper. By applying the comparison theorem of diferential equations and constructing a suitable Lyapunov function, a set of s...A nonautonomous ratio-dependent Leslie system incorporating a prey refuge is studied in this paper. By applying the comparison theorem of diferential equations and constructing a suitable Lyapunov function, a set of sufcient conditions which guarantee the persistent property and global attractivity of the system is obtained. Also, by applying the comparison theorem of diferential equations and Fluctuation Lemma, a set of sufcient conditions which ensure the extinction of the prey species and the global attractivity of predator species is obtained. This result shows that for the Lotka-Volterra type predator-prey system, when the value of prey refuge increases, predator species will be driven to extinction due to the lack of food. Our study shows that the alternative food resource predator species is always permanent, which means that prey refuge has no infuence on the permanence of predator species. However, refuge plays an important role in the persistent property of the prey species: large enough prey refuge could keep the persistent property of the prey species, while small enough refuge could lead to the extinction of prey species. Numerical simulations show the feasibility of the main results.展开更多
A two species Lotka-Volterra competitive system with infinite delays and feedback controls is studied in this paper.By constructing a suitable Lyapunov functional,we show that if the Lotka-Volterra competitive system ...A two species Lotka-Volterra competitive system with infinite delays and feedback controls is studied in this paper.By constructing a suitable Lyapunov functional,we show that if the Lotka-Volterra competitive system is bistable(in the absence of feedback controls),then by choosing some suitable values of feedback control variables,one of the species is driven to extinction while the other one becomes globally stable.Examples together with their numerical simulations are presented to verify the feasibility of our results.Our results not only improve but also complement those of Z.Li,M.A.Han and F.D.Chen[Influence of feedback controls on an autonomous Lotka-Volterra competitive system with infinite delays,Nonlinear Anal.:Real World Appl.,14(2013),402-413].展开更多
A non-autonomous allelopathic phytoplankton model with feedback controls is considered in this paper. By constructing some suitable Lyapunov type extinction functions, some sufficient conditions for the extinction of ...A non-autonomous allelopathic phytoplankton model with feedback controls is considered in this paper. By constructing some suitable Lyapunov type extinction functions, some sufficient conditions for the extinction of the system are obtained. For the autonomous case, by constructing a suitable Lyapunov function, we show that one species is extinct and the rest species is globally attractive. Our results supplement some known results.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 National Natural Science Foundation of China under Grant(11601085)the Natural Science Foundation of Fujian Province(2019J01783)
文摘Traditional May type cooperative model incorporating Michaelis-Menten type harvesting is proposed and studied in this paper. Sufficient conditions which ensure the extinction of the first species and the existence of a unique globally attractive positive equilibrium are obtained, respectively. Numeric simulations are carried out to show the feasibility of the main results.
文摘In this paper, we consider a modified Leslie-Clower predator prey model with Holling- type II schemes and mutual interference. By applying the comparison theorem of the differential equation and constructing a suitable Lyapunov function, sufficient conditions which guarantee the permanence and existence of a unique globally attractive positive almost periodic solution of the system are obtained. Our results not only supplement but also improve some existing ones.
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 National Natural Science Foundation of China under Grant(11601085)the Natural Science Foundation of Fujian Province(2017J01400)
文摘We revisit the stability property of an ecological system consisting of a predator and stage structure prey which was proposed by Raid Kamel Naji and Salam Jasim Majeed. By constructing some suitable Lyapunov function and applying the differential inequality theory, we show that the conditions which ensure the local stability of the vanishing point are enough to ensure its global stability. Our result supplements and complements some known results.
基金supported by the Natural Science Foundation of Fujian Province(2015J01012,2015J01019)
文摘In this paper, the almost periodic predator-prey-mutualist model with Holling type II functional response is discussed. A set of sufficient condi- tions which guarantee the uniform persistence and the global attractivity of the system are obtained. For the almost periodic case, by constructing a suit- able Lyapunov function, sufficient conditions which guarantee the existence of a unique globally attractive positive almost periodic solution of the system are obtained. An example together with its numerical simulations shows the feasibility of the main results.
文摘A nonautonomous ratio-dependent Leslie system incorporating a prey refuge is studied in this paper. By applying the comparison theorem of diferential equations and constructing a suitable Lyapunov function, a set of sufcient conditions which guarantee the persistent property and global attractivity of the system is obtained. Also, by applying the comparison theorem of diferential equations and Fluctuation Lemma, a set of sufcient conditions which ensure the extinction of the prey species and the global attractivity of predator species is obtained. This result shows that for the Lotka-Volterra type predator-prey system, when the value of prey refuge increases, predator species will be driven to extinction due to the lack of food. Our study shows that the alternative food resource predator species is always permanent, which means that prey refuge has no infuence on the permanence of predator species. However, refuge plays an important role in the persistent property of the prey species: large enough prey refuge could keep the persistent property of the prey species, while small enough refuge could lead to the extinction of prey species. Numerical simulations show the feasibility of the main results.
基金supported by the Natural Science Foundation of Fujian Province(2011J01007)the Technology Innovation Platform Project of Fujian Province(2009J1007)
文摘A two species Lotka-Volterra competitive system with infinite delays and feedback controls is studied in this paper.By constructing a suitable Lyapunov functional,we show that if the Lotka-Volterra competitive system is bistable(in the absence of feedback controls),then by choosing some suitable values of feedback control variables,one of the species is driven to extinction while the other one becomes globally stable.Examples together with their numerical simulations are presented to verify the feasibility of our results.Our results not only improve but also complement those of Z.Li,M.A.Han and F.D.Chen[Influence of feedback controls on an autonomous Lotka-Volterra competitive system with infinite delays,Nonlinear Anal.:Real World Appl.,14(2013),402-413].
基金supported by the Natural Science Foundation of Fujian Province(2011J010007,2013J01011,2013J01010)the Foundation of Fujian Education Bureau(JA12051,JA13361)
文摘A non-autonomous allelopathic phytoplankton model with feedback controls is considered in this paper. By constructing some suitable Lyapunov type extinction functions, some sufficient conditions for the extinction of the system are obtained. For the autonomous case, by constructing a suitable Lyapunov function, we show that one species is extinct and the rest species is globally attractive. Our results supplement some known results.
