Global attractivity of positive periodic solutions for nonlinear impulsive systems

In this paper, the existence, uniqueness and global attractivity of positive periodic solutions for nonlinear impulsive systems are studied. Firstly, existence conditions are established by the method of lower and upper solutions. Then uniqueness and global attractivity are obtained by developing the theories of monotone and concave operators. And lastly, the method and the results are applied to the impulsive n$n$-species cooperative Lotka–Volterra system and a model of a single-species dispersal among n$n$-patches.     

Global attractivity for impulsive population dynamics with delay arguments

This article investigates the global attractivity for impulsive population dynamics with delay arguments. Several sufficient conditions are obtained to ensure the global attractivity of the zero solution. These conditions do not require the boundedness of delay arguments, nor do they require some strict conditions on impulsive functions.     

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.     

Existence of periodic solutions,global attractivity and oscillation of impulsive delay population model

In this paper we consider the nonlinear impulsive delay population model. The main objective is to systematically study the qualitative behavior of the model including existence of periodic solutions, global attractivity and oscillation. The main oscillation results are the results of the prevalence of the mature cells about the periodic solutions and the global attractivity results are the conditions for nonexistence of dynamical diseases on the population.     

Global attractivity and positive almost periodic solution for delay logistic differential equation

In this paper, we establish some sufficient conditions for the global attractivity of positive solutions and the unique existence of positive almost periodic solutions for delay logistic differential equations of the form

x^′(t)=r(t)x(t)(a(t)−b(t)x(t)−L(_xt)).$x^{\prime }\left(t\right)=r\left(t\right)x\left(t\right)(a\left(t\right)-b\left(t\right)x\left(t\right)-L\left(x_t\right))\text{.}$

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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Almost periodic solutions for an impulsive delay Nicholson’s blowflies model

By means of the contraction mapping principle and Gronwall-Bellman’s inequality, we prove the existence and exponential stability of positive almost periodic solution for an impulsive delay Nicholson’s blowflies model. The main results are illustrated by an example.     

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.     

Global attractivity of a positive periodic solution for a nonautonomous stage structured population dynamics with time delay and diffusion

By employing the continuation theorem of coincidence degree theory, the existence of a positive periodic solution for a nonautonomous stage structured population dynamics with time delay and diffusion is established. Further, by constructing a Lyapunov functional and using the result of the existence of positive periodic solution, the attractivity of a positive periodic solution for above system is obtained.     

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 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

     

Global attractivity and positive almost periodic solution of a single species population model

3/2-criterion is built, which guarantees the global attractivity of positive solution for equation having the form x^′(t)=a(t)x(t)(1−L(t,xt)), where a(t)?0 and the linear functional L(t,⋅) is positive. Moreover, when the equation is almost periodic, the similar conditions can also guarantee the existence and uniqueness of almost periodic solution that is globally attractive. Our results improve those in literature.     

Almost periodic solutions for impulsive neural networks with delay

In the present paper the problems of existence and uniqueness of almost periodic solutions for impulsive cellular neural networks with delay are considered.     

Existence of positive periodic solutions for an impulsive semi-ratio-dependent predator-prey model with dispersion and time delays

In this paper, we propose an impulsive semi-ratio-dependent predator-prey model with dispersion and time delays. By applying the continuation theorem of coincidence degree theory, we establish a set of sufficient conditions on the existence of at least one positive periodic solution. The result not only improves but also generalizes that for the case without pulses.     

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…     

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.     

Globally exponential stability of periodic solutions for nonlinear impulsive delay systems

In this paper, the existence and globally exponential stability of periodic solutions for nonlinear impulsive delay systems are studied. Our results improve and generalize some of the previous results found in the literature. Two examples are discussed to illustrate our results.