We study the global dynamics of a rational diference equation with higher order,which includes many rational diference equations as its special cases.By some complicate computations and mathematical skills,we show tha...We study the global dynamics of a rational diference equation with higher order,which includes many rational diference equations as its special cases.By some complicate computations and mathematical skills,we show that its unique nonnegative fixed point is globally attractive.As application,our results not only improve many known ones,but also solve several“Open Problems and Conjectures”given by Professors Ladas and Camouzis,et al.展开更多
Several new sufficient conditions are given for the global attractivity of solutions of a kind of delay difference equations. They either include or improve some known results and put the study of Ladas' conjectur...Several new sufficient conditions are given for the global attractivity of solutions of a kind of delay difference equations. They either include or improve some known results and put the study of Ladas' conjecture forward.展开更多
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
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
In this paper, we consider a discrete Nicholson＇s blowflies model with delay. By constructing suitable Lyapunov functional, a sufficient condition for the permanence and global attractivity of the system is obtained....In this paper, we consider a discrete Nicholson＇s blowflies model with delay. By constructing suitable Lyapunov functional, a sufficient condition for the permanence and global attractivity of the system is obtained. An example together with its numerical simulation shows the feasibility of our main results.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
In this paper,the asymptotic behavior of three types of population models with delays and diffusion is studied.The first represents one species growth in the patchΩand periodic environment and with delays recruitment...In this paper,the asymptotic behavior of three types of population models with delays and diffusion is studied.The first represents one species growth in the patchΩand periodic environment and with delays recruitment,the second models a single species dispersal among the m patches of a heterogeneous environment,and the third models the spread of bacterial infections.Sufficient conditions for the global attractivity of periodic solution are obtained by the method of monotone theory and strongly concave operators.Some earlier results are extended to population models with delays and diffusion.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.
A new sufficient condition is given for the global attractivity of solutions ofthe delay difference equation xn+1= xnf(xn, zn-1), n = 0,1…,As an application, ourresults partly confirm a conjecture of G. Ladas.
This paper discusses a randomized Logistic equation $\dot N(t) = (r + \alpha \dot B(t))N(t)[1 - \frac{{N(t)}}{K}]$ with an initial value N(0) = N 0, and N 0 is a random variable satisfying 0 < N 0 < K. The exist...This paper discusses a randomized Logistic equation $\dot N(t) = (r + \alpha \dot B(t))N(t)[1 - \frac{{N(t)}}{K}]$ with an initial value N(0) = N 0, and N 0 is a random variable satisfying 0 < N 0 < K. The existence, uniqueness and global attractivity of positive solutions and maximum likelihood estimate (MLE) of the parameters of the equation are studied.展开更多
In this paper, we consider a nonautonomous competitive model with dispersion and a finite number of discrete delays. The system, which consists of two Lotka-Volterra patches, has two competitors: one can disperse betw...In this paper, we consider a nonautonomous competitive model with dispersion and a finite number of discrete delays. The system, which consists of two Lotka-Volterra patches, has two competitors: one can disperse between the two patches, but the other is confined to one patch and cannot disperse. Our purpose is to demonstrate that the dispersion rates have no effect on the uniform persistence of the solutions of the system. Furthermore, we establish the conditions under which the system admits a positive periodic solution which attracts all solutions.展开更多
This paper studies the nonlinear delay impulsive respiratory dynamics model. The model describes the sudden changes of the concentration of CO2 in the blood of the mammal. It is proved that the model has a unique posi...This paper studies the nonlinear delay impulsive respiratory dynamics model. The model describes the sudden changes of the concentration of CO2 in the blood of the mammal. It is proved that the model has a unique positive periodic solution. Somesufficient conditions for oscillation of all positive solutions about the positive periodic solution are established and also some sufficient conditions for the global attractivityof the periodic solution are obtained.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
基金Supported by the National Natural Science Foundation of China(61473340)Distinguished Professor Foundation of Qianjiang Scholar in Zhejiang Province(F703108L02)。
文摘We study the global dynamics of a rational diference equation with higher order,which includes many rational diference equations as its special cases.By some complicate computations and mathematical skills,we show that its unique nonnegative fixed point is globally attractive.As application,our results not only improve many known ones,but also solve several“Open Problems and Conjectures”given by Professors Ladas and Camouzis,et al.
文摘Several new sufficient conditions are given for the global attractivity of solutions of a kind of delay difference equations. They either include or improve some known results and put the study of Ladas' conjecture forward.
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Supported by the Natural Science Foundation of Fujian Province(Grant No.2015J01012)
文摘In this paper, we consider a discrete Nicholson＇s blowflies model with delay. By constructing suitable Lyapunov functional, a sufficient condition for the permanence and global attractivity of the system is obtained. An example together with its numerical simulation shows the feasibility of our main results.
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This research is supported by the Developing Fund of Nanjing University of Science and Technology.
文摘In this paper,the asymptotic behavior of three types of population models with delays and diffusion is studied.The first represents one species growth in the patchΩand periodic environment and with delays recruitment,the second models a single species dispersal among the m patches of a heterogeneous environment,and the third models the spread of bacterial infections.Sufficient conditions for the global attractivity of periodic solution are obtained by the method of monotone theory and strongly concave operators.Some earlier results are extended to population models with delays and diffusion.
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 NNSFC(10071022),Mathematical Tianyuan Foundation of China(Ty10026002-01-05-03)Shanghai Priority Academic Discipline.
文摘A new sufficient condition is given for the global attractivity of solutions ofthe delay difference equation xn+1= xnf(xn, zn-1), n = 0,1…,As an application, ourresults partly confirm a conjecture of G. Ladas.
基金This work was partially supported by the National Natural Science Foundation of China(Grant Nos.10431010 and 10571021)the Key Laboratory for Applied Statistics of Ministry of Education of China(KLAS)
文摘This paper discusses a randomized Logistic equation $\dot N(t) = (r + \alpha \dot B(t))N(t)[1 - \frac{{N(t)}}{K}]$ with an initial value N(0) = N 0, and N 0 is a random variable satisfying 0 < N 0 < K. The existence, uniqueness and global attractivity of positive solutions and maximum likelihood estimate (MLE) of the parameters of the equation are studied.
基金This research is supported by the National Natural Science Foundation of China the Natural Science Foundation of Henan Province.
文摘In this paper, we consider a nonautonomous competitive model with dispersion and a finite number of discrete delays. The system, which consists of two Lotka-Volterra patches, has two competitors: one can disperse between the two patches, but the other is confined to one patch and cannot disperse. Our purpose is to demonstrate that the dispersion rates have no effect on the uniform persistence of the solutions of the system. Furthermore, we establish the conditions under which the system admits a positive periodic solution which attracts all solutions.
文摘This paper studies the nonlinear delay impulsive respiratory dynamics model. The model describes the sudden changes of the concentration of CO2 in the blood of the mammal. It is proved that the model has a unique positive periodic solution. Somesufficient conditions for oscillation of all positive solutions about the positive periodic solution are established and also some sufficient conditions for the global attractivityof the periodic solution are obtained.
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.
