Existence and global attractivity of unique positive periodic solution for a model of hematopoiesis

In this paper, we consider the generalized model of hematopoiesis

     

Existence and global attractivity of unique positive almost periodic solution for a model of hematopoiesis

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.     

Permanence and global attractivity of an impulsive delay Logistic model

In this paper, we consider an impulsive delay Logistic model. First by mathematical analysis, we obtain the maximum and minimum values of solutions of the corresponding autonomous Logistic model. Then by applying the comparison theorem and constructing some suitable Lyapunov functionals, we discuss the permanence and the global attractivity of the model, based on the boundedness of solutions of the corresponding autonomous Logistic model. An example together with its numerical simulation is given to verify our main result.     

EXISTENCE AND GLOBAL ATTRACTIVITY OF PERIODIC SOLUTION OF A MODEL IN POPULATION DYNAMICS

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Existence and global attractivity of a positive periodic solution of a class of delay differential equation

The existence and the global attractivity of a positive periodic solution of the delay differential equationy(t)=y(t) F[t, y](t-τ ₁ (t)),⋯,y(t−τ _n (t))] are studied by using some techniques of the Mawhin coincidence degree theory and the constructing suitable Liapunov functionals. When these results are applied to some special delay bio-mathematics models, some new results are obtained, and many known results are improved. Project partially supported by the National Natural Science Foundation of China (Grant No. 10572057) and the Applied Basic Research Foundation of Yunnan Province.     

A note on global attractivity in models of hematopoiesis

We consider the delay differential equations which were proposed by Mackey and Glass as a model of blood cell production. We suggest new conditions sufficient for the positive equilibrium of the equation considered to be a global attractor. In contrast to the Lasota-Wazewska model, we establish the existence of the number δ_j = δ_j(n, τ) > 0 such that the equilibrium of the equation under consideration is a global attractor for all δ ε (0, δ_j] independently of β₀ and θ. Published in Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 1, pp. 5–12, January, 1998.     

Existence and global attractivity of almost periodic solutions for neural field with time delay

In this paper, the problem of existence and attractivity of almost periodic solutions for delayed neural field (DNF) with variable coefficients is discussed. First, the model of DNF is established as a modified neural field model. Secondly, by combining the theory of the exponential dichotomy, employing Banach fixed point theory and using differential inequality technique, some conditions for the the existence and attractivity of almost periodic solutions for the DNF are proposed.     

Global attractivity in a discrete delay logistic model

1.IntroductionIntherecentworks[l--31,theauthorsconsideredthediscretedelaylogisticmodelIn[3],itwasshownthateverypositivesolutionof(l)oscillatesaboutitspositiveequilibriumx~(a--1)/0ifandonlyifIn[if(seealso[2]),itwasprovedthatiftheneverypositivesolutionof(1)tendstox~(or--1)/pasn-- co.Thepurposeofthispaperistoobtainanothersufficieatconditionforthepositiveequilibriumxof(1)tobeaglobalattractorbyusingamethodverydmerelltfromthatusedin[1,21.Themainresultofthispaperisthefollowingtheorem.*Thisworkispart…     

Oscillation and attractivity in a discrete model with quadratic nonlinearity

Let a, c [euro] (0, ∞), b [euro] [IML0001] and let k be a nonnegative integer. We obtain necessary and sufficient conditions for all positive solutions of the nonlinear difference equation [IML0002] to oscillate about its positive equilibrium. When k = 0, we obtain necessary and sufficient conditions for the positive equilibrium of Eq. (?) to be a global attractor of all positive solutions.     

Existence and global attractivity of positive periodic solution for an impulsive Lasota-Wazewska model

Sufficient conditions are obtained for the existence and global attractivity of periodic positive solution of an impulsive Lasota-Wazewska model for the survival of red blood cells.     

Global attractivity of the almost periodic solution of a delay logistic population model with impulses

In this paper, we study the existence of almost periodic solutions of a delay logistic model with fixed moments of impulsive perturbations. By using a comparison theorem and constructing a suitable Lyapunov functional, a set of sufficient conditions for the existence and global attractivity of a unique positive almost periodic solution is obtained. As applications, some special models are studied; our new results improve and generalize former results.     

Existence and global attractivity of positive periodic solutions for delay Lotka-Volterra competition patch systems with stocking

By means of Mawhin's continuation theorem of coincidence degree and Lyapunov functional, a set of easily verifiable criteria are established for the existence and global attractivity of positive periodic solutions for delay Lotka-Volterra competition patch system with stocking

     

Existence and global attractivity of periodic solution for an impulsive delay differential equation with Allee effect

Sufficient conditions are obtained for the existence and global attractivity of positive periodic solution of an impulsive delay differential equation with Allee effect. The results of this paper improve and generalize noticeably the known theorems in the literature.     

Existence and global attractivity of a periodic solution for a prey–predator model with sex-structure

In this paper, we investigate the following periodic sex-structure model:

The sufficient and realistic conditions are obtained for the existence of positive periodic solution of above system. Further, by constructing a V functional and using the result of the existence of positive periodic solutions, the global attractivity of a positive periodic solution for above system is obtained.     

Permanence and global attractivity for facultative mutualism system with delay

In this paper, we consider a facultative mutualism system with different delays. Sufficient criteria for permanence and global attractivity for the system are established. Ultimate uniform boundedness of the solutions ensures permanence. For the global attractivity of the system, magnitude of the delays plays a major role. Copyright © 2003 John Wiley & Sons, Ltd.     

Hopfield神经网络的周期解存在性及其全局吸引性

利用重合度理论和微分不等式分析等技巧，给出了Hopfield神经网络周期解存在性及其全局吸引性的判别准则。     

Global attractivity of positive periodic solution to periodic Lotka-Volterra competition systems with pure delay

We consider a periodic Lotka-Volterra competition system without instantaneous negative feedbacks (i.e., pure-delay systems)

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