In this paper, the qualitative properties of general nonautonomous Lotka-Volterran-species competitive systems with impulsive e?ects are studied. Some new criteria on thepermanence, extinction and global attractivity ...In this paper, the qualitative properties of general nonautonomous Lotka-Volterran-species competitive systems with impulsive e?ects are studied. Some new criteria on thepermanence, extinction and global attractivity of partial species are established by used themethods of inequalities estimate and Liapunov functions. As applications, nonautonomous twospecies Lotka-Volterra systems with impulses are discussed.展开更多
In this paper we prove a global attractivity result for the unique positive equilibrium point of a difference equation,which improves and generalizes some known ones in the existing literature.Especially,our results c...In this paper we prove a global attractivity result for the unique positive equilibrium point of a difference equation,which improves and generalizes some known ones in the existing literature.Especially,our results completely solve an open problem and some conjectures proposed in[1,2,3,4].展开更多
In this paper, a stochastic two-prey one-predator model with <em>S</em>-type distributed time delays and Lévy noises is considered. Using the comparison theorem and Ito’s formula, sufficient conditio...In this paper, a stochastic two-prey one-predator model with <em>S</em>-type distributed time delays and Lévy noises is considered. Using the comparison theorem and Ito’s formula, sufficient conditions of persistence in the mean and extinct for each population are established. Then, conditions of global attractivity and stability in distribution by Barbalat’s conclusion are also obtained. Furthermore, Euler numerical simulation method is given to demonstrate our conclusions.展开更多
This paper is intended to investigate a class of Nicholson's blowflies system with patch structure and multiple pairs of distinct time-varying delays,we are interested in finding the infuence of the distinct time-...This paper is intended to investigate a class of Nicholson's blowflies system with patch structure and multiple pairs of distinct time-varying delays,we are interested in finding the infuence of the distinct time-varying delays in the same reproductive function on its asymptotic behavior.By using the theory of functional differential equations,the fluctuation lemma,and the technique of differential inequalities,some new delay-dependent criteria on the global attractivity of the positive equilibrium point are established.In addition,the effectiveness and feasibility of the theoretical achievements are illustrated by some numerical simulations.展开更多
In this paper, to complete the global dynamics of a multi-strains SIS epidemic model, we establish a precise result on coexistence for the cases of the partial and complete duplicated multiple largest reproduction rat...In this paper, to complete the global dynamics of a multi-strains SIS epidemic model, we establish a precise result on coexistence for the cases of the partial and complete duplicated multiple largest reproduction ratios for this model.展开更多
A delayed predator-prey model concerning impulsive spraying pesticides and releasing natural enemies is proposed and investigated,in which both the prey and the predator have a history that takes them through two stag...A delayed predator-prey model concerning impulsive spraying pesticides and releasing natural enemies is proposed and investigated,in which both the prey and the predator have a history that takes them through two stages:immature and mature.The global attractiveness of the pest-eradication periodic solution is discussed,and sufficient condition is obtained for the permanence of the system.Further,numerical simulations show that there is a characteristic sequence of bifurcations leading to a chaotic dynamics,which implies that the system with constant periodic impulsive perturbations admits rich and complex dynamics.展开更多
A new fixed point theorem is presented and sufficient conditions are obtained for the existence, uniqueness and global attractivity of a positive almost periodic solution to a delayed differential equation with almost...A new fixed point theorem is presented and sufficient conditions are obtained for the existence, uniqueness and global attractivity of a positive almost periodic solution to a delayed differential equation with almost periodic factors.展开更多
In a polluted environment, considering the biological population infected with a kind of disease and hunted by human beings, we formulate a nonautonomous SIR population-epidemic model with time-varying impulsive relea...In a polluted environment, considering the biological population infected with a kind of disease and hunted by human beings, we formulate a nonautonomous SIR population-epidemic model with time-varying impulsive release and general nonlinear incidence rate and investigate dynamical behaviors of the model. Under the reasonable assumptions, the sufficient conditions which guarantee the globally attractive of the disease-free periodic solution and the permanence of the infected fish are established, that is, the infected fish dies out if , whereas the disease persists if . To substantiate our theoretical results, extensive numerical simulations are performed for a hypothetical set of parameter values.展开更多
In this paper, a nonlinear discrete two species competitive system is considered. Sufficient conditions which guarantee that one of components is driven to extinction while the other is globally attractive are obtained.
In this paper, the almost periodic predator-prey-mutualist model with Holling type II functional response is discussed. A set of sufficient conditions which guarantee the uniform persistence and the global attractivit...In this paper, the almost periodic predator-prey-mutualist model with Holling type II functional response is discussed. A set of sufficient conditions which guarantee the uniform persistence and the global attractivity of the system are obtained. For the almost periodic case, by constructing a suitable 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 class of non-autonomous two species Lotka-Volterra competitive system with pure discrete time delays is discussed. Some sufficient conditions on the boundedness, permanence, periodic solution and global attractivity...A class of non-autonomous two species Lotka-Volterra competitive system with pure discrete time delays is discussed. Some sufficient conditions on the boundedness, permanence, periodic solution and global attractivity of the system are established by means of the comparison method and Liapunov functional.展开更多
In this paper,we analyze the global dynamics of a neoclassical growth system incorporating patch structure and multiple pairs of time-varying delays.First,we derive the global existence,positiveness and boundedness of...In this paper,we analyze the global dynamics of a neoclassical growth system incorporating patch structure and multiple pairs of time-varying delays.First,we derive the global existence,positiveness and boundedness of solutions for the addressed system.Then,by employing some novel differential inequality analyses and the fluctuation lemma,both delay-independent and delay-dependent criteria are established to ensure that all solutions are convergent to a unique positive equilibrium point vector,which does not possess the same components.Our results supplement and improve some existing results.Ultimately,some numerical examples are afforded to prove the effectiveness and feasibility of the theoretical findings.展开更多
This paper considers a feedback control systems of differential equations with delays. By applying the differential inequality theorem, sufficient conditions for the permanence of the system are obtained. Also, by con...This paper considers a feedback control systems of differential equations with delays. By applying the differential inequality theorem, sufficient conditions for the permanence of the system are obtained. Also, by constructing a suitable Lyapunov functional, a criterion for the global stability of the model is obtained.展开更多
By means of the Banach fixed point principle,we establish some sufficient conditions ensuring the existence of the global attracting sets and the exponential decay in the mean square of mild solutions for a class of n...By means of the Banach fixed point principle,we establish some sufficient conditions ensuring the existence of the global attracting sets and the exponential decay in the mean square of mild solutions for a class of neutral stochastic functional differential equations by Poisson jumps.An example is presented to illustrate the effectiveness of the obtained result.展开更多
In this paper,we are concerned with a class of impulsive neutral stochastic functional different equations driven by tempered fractional Brownian motion in the Hilbert space.We obtain the global attracting and quasi-i...In this paper,we are concerned with a class of impulsive neutral stochastic functional different equations driven by tempered fractional Brownian motion in the Hilbert space.We obtain the global attracting and quasi-invariant sets of the considered equations driven by tempered fractional Brownian motion B^(α,λ)(t)with 0<α<1/2 andλ>0.In particular,we give some sufficient conditions which ensure the exponential decay in the p-th moment of the mild solution of the considered equations.Finally,an example is given to illustrate the feasibility and effectiveness of the results obtained.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 the permanence of asymptotically periodic mul-tispecies Lotka-Volterra competition predator-prey system. By means of the standard comparison theorem, we improve or extend the corresponding r...In this paper, we consider the permanence of asymptotically periodic mul-tispecies Lotka-Volterra competition predator-prey system. By means of the standard comparison theorem, we improve or extend the corresponding results given by Peng and Chen [1], Teng and Li [2], Zhao and Chen [3]. Also, we obtain the conditions which ensure the permanence and global attractivity of asymptotically periodic multispecies competition predator-prey system.展开更多
An autonomous stage-structured competitive systems with toxic effect is investigated in this paper. Sufficient conditions which guarantee the global attractivity of the system and the extinction of the partial species...An autonomous stage-structured competitive systems with toxic effect is investigated in this paper. Sufficient conditions which guarantee the global attractivity of the system and the extinction of the partial species are obtained,respectively. Our results supplement and compliment one of the main results of Liu and Li [Global stability analysis of a nonautonomous stage-structured competitive system with toxic effect and double maturation delays, Abstract and Applied Analysis, Volume 2014, Article ID 689573, 15 pages].展开更多
Although the incidence of measles has been significantly reduced through vaccination,it remains an important public health problem.In this paper,a measles model with pulse vaccination is formulated to investigate the ...Although the incidence of measles has been significantly reduced through vaccination,it remains an important public health problem.In this paper,a measles model with pulse vaccination is formulated to investigate the influential pulse vaccination on the period of time for the extinction of the disease.The threshold value of the formulated model,called the control reproduction number and denoted by R^(*),is derived.It is found that the disease-free periodic solution of the model exists and is globally attractivity whenever R^(*)<1 in the sense that measles is eliminated.If R^(*)>1,the positive solution of the model exists and is permanent which indicates the disease persists in the community.Theoretical conditions for disease eradication under various constraints are given.The effect of pulse vaccination is explored using data from Thailand.The results obtained can guide policymakers in deciding on the optimal scheduling in order to achieve the strategic plan of measles elimination by vaccination.展开更多
基金Supported by The National Natural Science Foundation of P.R. China [60764003]The Scientific Research Programmes of Colleges in Xinjiang [XJEDU2007G01, XJEDU2006I05]+1 种基金The National Key Technologies R & D Program of China [2008BAI68B01]The Natural Science Foundation of Jiangxi Province [2008GZS0027]
文摘In this paper, the qualitative properties of general nonautonomous Lotka-Volterran-species competitive systems with impulsive e?ects are studied. Some new criteria on thepermanence, extinction and global attractivity of partial species are established by used themethods of inequalities estimate and Liapunov functions. As applications, nonautonomous twospecies Lotka-Volterra systems with impulses are discussed.
基金the National Natural Science Foundation of China(61473340)the Distinguished Professor Foundation of Qianjiang Scholar in Zhejiang Province+1 种基金the National Natural Science Foundation of Zhejiang Province(LQ13A010019)the National Natural Science Foundation of Zhejiang University of Science and Technology(F701108G14).
文摘In this paper we prove a global attractivity result for the unique positive equilibrium point of a difference equation,which improves and generalizes some known ones in the existing literature.Especially,our results completely solve an open problem and some conjectures proposed in[1,2,3,4].
文摘In this paper, a stochastic two-prey one-predator model with <em>S</em>-type distributed time delays and Lévy noises is considered. Using the comparison theorem and Ito’s formula, sufficient conditions of persistence in the mean and extinct for each population are established. Then, conditions of global attractivity and stability in distribution by Barbalat’s conclusion are also obtained. Furthermore, Euler numerical simulation method is given to demonstrate our conclusions.
基金This work was supposed by Jiaxing public welfare research program(2022AD30113).
文摘This paper is intended to investigate a class of Nicholson's blowflies system with patch structure and multiple pairs of distinct time-varying delays,we are interested in finding the infuence of the distinct time-varying delays in the same reproductive function on its asymptotic behavior.By using the theory of functional differential equations,the fluctuation lemma,and the technique of differential inequalities,some new delay-dependent criteria on the global attractivity of the positive equilibrium point are established.In addition,the effectiveness and feasibility of the theoretical achievements are illustrated by some numerical simulations.
文摘In this paper, to complete the global dynamics of a multi-strains SIS epidemic model, we establish a precise result on coexistence for the cases of the partial and complete duplicated multiple largest reproduction ratios for this model.
基金Foundation item： Supported by the NNSF of China（11071254） Supported by the Science Foundation of Mechanical Engineering College（YJJXMll004）
文摘A delayed predator-prey model concerning impulsive spraying pesticides and releasing natural enemies is proposed and investigated,in which both the prey and the predator have a history that takes them through two stages:immature and mature.The global attractiveness of the pest-eradication periodic solution is discussed,and sufficient condition is obtained for the permanence of the system.Further,numerical simulations show that there is a characteristic sequence of bifurcations leading to a chaotic dynamics,which implies that the system with constant periodic impulsive perturbations admits rich and complex dynamics.
基金supported by the NNSF of China (10571064)the research Foundation of the Doctoral Program of Higher Education of China (20094407110001)the NSF of Guangdong Province (10151063101000003)
文摘A new fixed point theorem is presented and sufficient conditions are obtained for the existence, uniqueness and global attractivity of a positive almost periodic solution to a delayed differential equation with almost periodic factors.
文摘In a polluted environment, considering the biological population infected with a kind of disease and hunted by human beings, we formulate a nonautonomous SIR population-epidemic model with time-varying impulsive release and general nonlinear incidence rate and investigate dynamical behaviors of the model. Under the reasonable assumptions, the sufficient conditions which guarantee the globally attractive of the disease-free periodic solution and the permanence of the infected fish are established, that is, the infected fish dies out if , whereas the disease persists if . To substantiate our theoretical results, extensive numerical simulations are performed for a hypothetical set of parameter values.
基金supported by Program for New Century Excellent Talents in Fujian Province University (0330-003383)
文摘In this paper, a nonlinear discrete two species competitive system is considered. Sufficient conditions which guarantee that one of components is driven to extinction while the other is globally attractive are obtained.
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 conditions which guarantee the uniform persistence and the global attractivity of the system are obtained. For the almost periodic case, by constructing a suitable 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 class of non-autonomous two species Lotka-Volterra competitive system with pure discrete time delays is discussed. Some sufficient conditions on the boundedness, permanence, periodic solution and global attractivity of the system are established by means of the comparison method and Liapunov functional.
文摘In this paper,we analyze the global dynamics of a neoclassical growth system incorporating patch structure and multiple pairs of time-varying delays.First,we derive the global existence,positiveness and boundedness of solutions for the addressed system.Then,by employing some novel differential inequality analyses and the fluctuation lemma,both delay-independent and delay-dependent criteria are established to ensure that all solutions are convergent to a unique positive equilibrium point vector,which does not possess the same components.Our results supplement and improve some existing results.Ultimately,some numerical examples are afforded to prove the effectiveness and feasibility of the theoretical findings.
基金This work is supported by the Foundation of Science and Technology of Fujian Province for Young Scholars (2004J0002) the Foundation of Fujian Education Bureau (JA04156).
文摘This paper considers a feedback control systems of differential equations with delays. By applying the differential inequality theorem, sufficient conditions for the permanence of the system are obtained. Also, by constructing a suitable Lyapunov functional, a criterion for the global stability of the model is obtained.
文摘By means of the Banach fixed point principle,we establish some sufficient conditions ensuring the existence of the global attracting sets and the exponential decay in the mean square of mild solutions for a class of neutral stochastic functional differential equations by Poisson jumps.An example is presented to illustrate the effectiveness of the obtained result.
基金partially supported by the NNSF of China(No.11901058)
文摘In this paper,we are concerned with a class of impulsive neutral stochastic functional different equations driven by tempered fractional Brownian motion in the Hilbert space.We obtain the global attracting and quasi-invariant sets of the considered equations driven by tempered fractional Brownian motion B^(α,λ)(t)with 0<α<1/2 andλ>0.In particular,we give some sufficient conditions which ensure the exponential decay in the p-th moment of the mild solution of the considered equations.Finally,an example is given to illustrate the feasibility and effectiveness of the results obtained.
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.
基金This work is supported by the Foundation of Science and Technology of Fujian Province for Young Scholars (2004J0002) the Foundation of Fujian Education Bureau (JA04156).
文摘In this paper, we consider the permanence of asymptotically periodic mul-tispecies Lotka-Volterra competition predator-prey system. By means of the standard comparison theorem, we improve or extend the corresponding results given by Peng and Chen [1], Teng and Li [2], Zhao and Chen [3]. Also, we obtain the conditions which ensure the permanence and global attractivity of asymptotically periodic multispecies competition predator-prey system.
基金supported by the Natural Science Foundation of Fujian Province(2015J01012,2015J01019)
文摘An autonomous stage-structured competitive systems with toxic effect is investigated in this paper. Sufficient conditions which guarantee the global attractivity of the system and the extinction of the partial species are obtained,respectively. Our results supplement and compliment one of the main results of Liu and Li [Global stability analysis of a nonautonomous stage-structured competitive system with toxic effect and double maturation delays, Abstract and Applied Analysis, Volume 2014, Article ID 689573, 15 pages].
基金the Petchra Pra Jom Klao Ph.D.research scholarship,King Mongkut's University of Technology Thonburi (KMUTT)for the financial support (No.31/2557).
文摘Although the incidence of measles has been significantly reduced through vaccination,it remains an important public health problem.In this paper,a measles model with pulse vaccination is formulated to investigate the influential pulse vaccination on the period of time for the extinction of the disease.The threshold value of the formulated model,called the control reproduction number and denoted by R^(*),is derived.It is found that the disease-free periodic solution of the model exists and is globally attractivity whenever R^(*)<1 in the sense that measles is eliminated.If R^(*)>1,the positive solution of the model exists and is permanent which indicates the disease persists in the community.Theoretical conditions for disease eradication under various constraints are given.The effect of pulse vaccination is explored using data from Thailand.The results obtained can guide policymakers in deciding on the optimal scheduling in order to achieve the strategic plan of measles elimination by vaccination.
