Sufficient conditions are obtained which guarantee the uniform persistence and global attractivity of solutions for the model of hematopoiesis. Then some criteria are established for the existence, uniqueness and glob...Sufficient conditions are obtained which guarantee the uniform persistence and global attractivity of solutions for the model of hematopoiesis. Then some criteria are established for the existence, uniqueness and global attractivity of almost periodic solutions of almost periodic system.展开更多
Some global properties such as global attractivity and global exponential stability for delayed Hopfield neural networks model, under the weaker assumptions on nonlinear activation functions, are concerned. By constru...Some global properties such as global attractivity and global exponential stability for delayed Hopfield neural networks model, under the weaker assumptions on nonlinear activation functions, are concerned. By constructing suitable Liapunov function, some simpler criteria for global attractivity and global exponential stability for Hopfield continuous neural network,; with time delays are presented.展开更多
In this paper the global attractivity of the nonlinear difference equationis investigated, where a,b, A ∈ (0,∞), k is an positive integer and the initial conditions x- k, …, x-1 and x0 are arbitrary positive number...In this paper the global attractivity of the nonlinear difference equationis investigated, where a,b, A ∈ (0,∞), k is an positive integer and the initial conditions x- k, …, x-1 and x0 are arbitrary positive numbers. It is shown that the unique positive equilibrium of the equation is global attractive. As a corollary, the result gives a positive confirmation on the conjecture presented by Kocic and Ladas [1,p154].展开更多
A neutral difference equation with positive and negative coefficientsΔ(x n-c nx n-k )+p nx n-l -q nx n-r =0, n=0,1,2,...,is considered and a sufficient condition for the global attractivity of the ze...A neutral difference equation with positive and negative coefficientsΔ(x n-c nx n-k )+p nx n-l -q nx n-r =0, n=0,1,2,...,is considered and a sufficient condition for the global attractivity of the zero solution of this equation is obtained, which improves and extends the all known results in the literature.展开更多
We investigate a stage-structured delayed predator-prey model with impulsive stocking on prey and continuous harvesting on predator. According to the fact of biological resource management, we improve the assumption o...We investigate a stage-structured delayed predator-prey model with impulsive stocking on prey and continuous harvesting on predator. According to the fact of biological resource management, we improve the assumption of a predator-prey model with stage structure for predator population that each individual predator has the same ability to capture prey. It is assumed that the immature and mature individuals of the predator population are divided by a fixed age, and immature predator population does not have the ability to attach prey. Sufficient conditions are obtained, which guarantee the global attractivity of predator-extinction periodic solution and the permanence of the system. Our results show that the behavior of impulsive stocking on prey plays an important role for the permanence of the system, and provide tactical basis for the biological resource management. Numerical analysis is presented to illuminate the dynamics of the system.展开更多
The global attractivity of the delay difference equation Deltax(n) + a(n)x(n) + f(n, Sigma(s = -k)(0)(q) over bar (s), (n) x(s + n)) = 0, which includes the discrete type of many mathematical ecological equations, was...The global attractivity of the delay difference equation Deltax(n) + a(n)x(n) + f(n, Sigma(s = -k)(0)(q) over bar (s), (n) x(s + n)) = 0, which includes the discrete type of many mathematical ecological equations, was discussed. The sufficient conditions that guarantee every solution to converge to zero are obtained. Many known results are improved and generated.展开更多
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
This paper studies the global attractivity of the positive equilibrium 1 of the delay logistic difference equation Δ y n=p ny n(1-y τ(n) ), n=0,1,2,...,(*)where {p n} is a sequence of positive real n...This paper studies the global attractivity of the positive equilibrium 1 of the delay logistic difference equation Δ y n=p ny n(1-y τ(n) ), n=0,1,2,...,(*)where {p n} is a sequence of positive real numbers, {τ(n)} is a nondecreasing sequence of integers, τ(n)<n and lim n→∞τ(n)=∞ .It is proved that ifnj=τ(n)p j≤54 for sufficiently large n and ∞j=0p j=∞,then all positive solutions of Eq.(*) tend to 1 as n→∞ .The results improve the existing results in literature.展开更多
Consider the discrete Lasota Wazewska modelN n+1 -N n =-μN n +pe -rN n-k , n=0,1,2,...(*)where μ∈(0,1),r,p∈(0,∞) and k ∈N.A sufficient condition for all positive solutions of (*) to...Consider the discrete Lasota Wazewska modelN n+1 -N n =-μN n +pe -rN n-k , n=0,1,2,...(*)where μ∈(0,1),r,p∈(0,∞) and k ∈N.A sufficient condition for all positive solutions of (*) to be attracted to its equilibrium N is obtained.It improves correspondent result obtained by Chen and Yu in 1999.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
Sufficient conditions are derived for the existence of globally asymptotically stable solution in a two species competition system with periodic coefficients and feedback controls.
In this paper, we study the existence and global attractivity of positive peri- odic solutions of a Logistic growth system with feedback control and deviating arguments. A sufficient condition is derived for the exist...In this paper, we study the existence and global attractivity of positive peri- odic solutions of a Logistic growth system with feedback control and deviating arguments. A sufficient condition is derived for the existence of a unique peri- odic solution with strictly positive components which is globally asymptotically stable by using the method of coincidence degree and Liapunov functional. Some new results are obtained. The known results are improved and generalized.展开更多
In this paper, we consider the N-species cooperation system with discrete time delays and feedback controls. By using the differential inequality theory and constructing a suitable Lyapunov functional, we obtain suffi...In this paper, we consider the N-species cooperation system with discrete time delays and feedback controls. By using the differential inequality theory and constructing a suitable Lyapunov functional, we obtain sufficient conditions which guarantee the permanence and the global attractivity of the system.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 this paper we further study the delay differential equation N .(t)=-δN(t)+pN(t-τ)e -aN(t-τ) , t0(*) used in describing the dynamics of Nicholson’s blowflies. When p】δ ,we establish new su...In this paper we further study the delay differential equation N .(t)=-δN(t)+pN(t-τ)e -aN(t-τ) , t0(*) used in describing the dynamics of Nicholson’s blowflies. When p】δ ,we establish new sufficient conditions for the positive equilibrium N * of (*) which is a global attractor.展开更多
This note considers the model for the survival of the red blood ceels with several delays and establishes some new sufficient conditions which guarantee the positive equilibrium of the model being a global attractor. ...This note considers the model for the survival of the red blood ceels with several delays and establishes some new sufficient conditions which guarantee the positive equilibrium of the model being a global attractor. Our results generalize and improve the corre-spondently known results obtained in [1, 3], and solve a conjecture in [7].展开更多
This paper studies the global attractivity of the difference equation where {pn} and {qn} are sequences of nonnegative real numbers, μ, τ and δ are nonnegative integers. We estabilish some sufficient conditions whi...This paper studies the global attractivity of the difference equation where {pn} and {qn} are sequences of nonnegative real numbers, μ, τ and δ are nonnegative integers. We estabilish some sufficient conditions which guarantee that all the solutions of (*) tend to zero as n tends to infinity.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 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
In this paper, a nonautonomous ratio-dependent multispecies competitionpredator system with Holling's Ⅲ type functional response is studied, where all parameters are time dependent. It is proved that the system is u...In this paper, a nonautonomous ratio-dependent multispecies competitionpredator system with Holling's Ⅲ type functional response is studied, where all parameters are time dependent. It is proved that the system is uniformly persistent under suitable condition. Furthermore, the sufficient conditions are established for global attractivity of a periodicsolution of the system. response展开更多
基金Supported by the NNSF of China(10671021)the SRF of Hunan Provincial Education Department(09C388)
文摘Sufficient conditions are obtained which guarantee the uniform persistence and global attractivity of solutions for the model of hematopoiesis. Then some criteria are established for the existence, uniqueness and global attractivity of almost periodic solutions of almost periodic system.
文摘Some global properties such as global attractivity and global exponential stability for delayed Hopfield neural networks model, under the weaker assumptions on nonlinear activation functions, are concerned. By constructing suitable Liapunov function, some simpler criteria for global attractivity and global exponential stability for Hopfield continuous neural network,; with time delays are presented.
文摘In this paper the global attractivity of the nonlinear difference equationis investigated, where a,b, A ∈ (0,∞), k is an positive integer and the initial conditions x- k, …, x-1 and x0 are arbitrary positive numbers. It is shown that the unique positive equilibrium of the equation is global attractive. As a corollary, the result gives a positive confirmation on the conjecture presented by Kocic and Ladas [1,p154].
基金the Science Foundation of Educational Committee of Hunan Provinc
文摘A neutral difference equation with positive and negative coefficientsΔ(x n-c nx n-k )+p nx n-l -q nx n-r =0, n=0,1,2,...,is considered and a sufficient condition for the global attractivity of the zero solution of this equation is obtained, which improves and extends the all known results in the literature.
基金the National Natural Science Foundation of China(No.10771179)the Emphasis Subject of Guizhou Province of China
文摘We investigate a stage-structured delayed predator-prey model with impulsive stocking on prey and continuous harvesting on predator. According to the fact of biological resource management, we improve the assumption of a predator-prey model with stage structure for predator population that each individual predator has the same ability to capture prey. It is assumed that the immature and mature individuals of the predator population are divided by a fixed age, and immature predator population does not have the ability to attach prey. Sufficient conditions are obtained, which guarantee the global attractivity of predator-extinction periodic solution and the permanence of the system. Our results show that the behavior of impulsive stocking on prey plays an important role for the permanence of the system, and provide tactical basis for the biological resource management. Numerical analysis is presented to illuminate the dynamics of the system.
文摘The global attractivity of the delay difference equation Deltax(n) + a(n)x(n) + f(n, Sigma(s = -k)(0)(q) over bar (s), (n) x(s + n)) = 0, which includes the discrete type of many mathematical ecological equations, was discussed. The sufficient conditions that guarantee every solution to converge to zero are obtained. Many known results are improved and generated.
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.
文摘This paper studies the global attractivity of the positive equilibrium 1 of the delay logistic difference equation Δ y n=p ny n(1-y τ(n) ), n=0,1,2,...,(*)where {p n} is a sequence of positive real numbers, {τ(n)} is a nondecreasing sequence of integers, τ(n)<n and lim n→∞τ(n)=∞ .It is proved that ifnj=τ(n)p j≤54 for sufficiently large n and ∞j=0p j=∞,then all positive solutions of Eq.(*) tend to 1 as n→∞ .The results improve the existing results in literature.
基金Supported by the Science Foundation of Educational Committee of Hunan Province
文摘Consider the discrete Lasota Wazewska modelN n+1 -N n =-μN n +pe -rN n-k , n=0,1,2,...(*)where μ∈(0,1),r,p∈(0,∞) and k ∈N.A sufficient condition for all positive solutions of (*) to be attracted to its equilibrium N is obtained.It improves correspondent result obtained by Chen and Yu in 1999.
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Sufficient conditions are derived for the existence of globally asymptotically stable solution in a two species competition system with periodic coefficients and feedback controls.
文摘In this paper, we study the existence and global attractivity of positive peri- odic solutions of a Logistic growth system with feedback control and deviating arguments. A sufficient condition is derived for the existence of a unique peri- odic solution with strictly positive components which is globally asymptotically stable by using the method of coincidence degree and Liapunov functional. Some new results are obtained. The known results are improved and generalized.
基金This work is supported by the Foundation of Fujian Education Bureau (JA04156).
文摘In this paper, we consider the N-species cooperation system with discrete time delays and feedback controls. By using the differential inequality theory and constructing a suitable Lyapunov functional, we obtain sufficient conditions which guarantee the permanence and the global attractivity of the system.
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 this paper we further study the delay differential equation N .(t)=-δN(t)+pN(t-τ)e -aN(t-τ) , t0(*) used in describing the dynamics of Nicholson’s blowflies. When p】δ ,we establish new sufficient conditions for the positive equilibrium N * of (*) which is a global attractor.
文摘This note considers the model for the survival of the red blood ceels with several delays and establishes some new sufficient conditions which guarantee the positive equilibrium of the model being a global attractor. Our results generalize and improve the corre-spondently known results obtained in [1, 3], and solve a conjecture in [7].
文摘This paper studies the global attractivity of the difference equation where {pn} and {qn} are sequences of nonnegative real numbers, μ, τ and δ are nonnegative integers. We estabilish some sufficient conditions which guarantee that all the solutions of (*) tend to zero as n tends to infinity.
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 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.
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, a nonautonomous ratio-dependent multispecies competitionpredator system with Holling's Ⅲ type functional response is studied, where all parameters are time dependent. It is proved that the system is uniformly persistent under suitable condition. Furthermore, the sufficient conditions are established for global attractivity of a periodicsolution of the system. response