Periodic solutions and oscillation of discrete non-linear delay population dynamics model with external force

^** Email: emelabbasy{at}mans.edu.eg^*** Email: shsaker{at}mans.edu.eg In this paper, we consider the discrete non-linear delay populationdynamics model [graphic: see PDF] where m is a positive integer, p(n), Q(n) and (n) are positiveperiodic sequences of period . By the method that involves theapplication of the Gaines and Mawhins coincidence degree theory,we prove that there exists a positive -periodic solution (n). We prove that every positive solutionof (*) which does not oscillate about (n)satisfies lim_t[y(n)–(n)]=0.We establish some necessary and sufficient conditions for theoscillation of every positive solution about (n), and finally, we establish the lower and upperbounds of the oscillatory solutions.     

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…     

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.     

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。     

Existence and global attractivity of positive periodic solutions of functional differential equations with feedback control

Sufficient conditions are obtained for the existence and global attractivity of positive periodic solutions of the delay differential system with feedback control

The method involves the application of Krasnoselskii's fixed point theorem and estimates of uniform upper and lower bounds of solutions. When these results are applied to some special delay population models with multiple delays, some new results are obtained and some known results are generalized.     

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

ＥＸＩＳＴＥＮＣＥＡＮＤＧＬＯＢＡＬＡＴＴＲＡＣＴＩＶＩＴＹＯＦＰＥＲＩＯＤＩＣＳＯＬＵＴＩＯＮＯＦＡＭＯＤＥＬＩＮＰＯＰＵＬＡＴＩＯＮＤＹＮＡＭＩＣＳ￥ＷＥＮＧＰＥＩＸＵＡＮ（佩萱）ＬＩＡＮＧＭＩＡＯＬＩＡＮ（梁妙莲）（ＤｅｐａｒｔｍｅｎｔｏｆＳｏ...     

Global attractivity and almost periodic solution of a discrete mutualism model with delays

In this paper, we consider an almost periodic discrete Lotka–Volterra mutualism model with delays. We first obtain the permanence and global attractivity of the system. By means of an almost periodic functional hull theory and constructing a suitable Lyapunov function, sufficient conditions are obtained for the existence of a unique strictly positive almost periodic solution, which is globally attractive. An example together with numerical simulation indicates the feasibility of the main result. Copyright © 2013 John Wiley & Sons, Ltd.     

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 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 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.     

The persistence and global attractivity in general nonautonomous discrete single-species Kolmogorov model with delays

In this paper, general nonautonomous discrete-time single-species Kolmogorov model with delays is studied. Some sufficient conditions on the boundedness, persistence, permanence and global attractivity of solutions are established. As application, the discrete time nonautonomous delayed Allee-effect model is discussed. The sufficient conditions on the permanence and global attractivity are obtained.     

一类时滞Logistic差分方程的全局吸引性

§ 1　ＩｎｔｒｏｄｕｃｔｉｏｎＣｏｎｓｉｄｅｒｔｈｅｎｏｎａｕｔｏｎｏｍｏｕｓｄｅｌａｙｌｏｇｉｓｔｉｃｄｉｆｆｅｒｅｎｃｅｅｑｕａｔｉｏｎΔｙｎ =ｐｎｙｎ( 1 - ｙτ(ｎ) )　 ,ｎ =0 ,1 ,2 ,...,( 1 1 )ｗｈｅｒｅｐｎ ∞ｎ =0 ｉｓａｓｅｑｕｅｎｃｅｏｆｐｏｓｉｔｉｖｅｒｅａｌｎｕｍｂｅｒｓ ,τ(ｎ) ∞ｎ =0 ｉｓａｎｏｎｄｅｃｒｅａｓｉｎｇｓｅｑｕｅｎｃｅｏｆｉｎｔｅｇｅｒｓ,τ(ｎ) <ｎａｎｄｌｉｍｎ→∞τ(ｎ) =∞ ,Δｙｎ=ｙｎ +1- ｙｎ.Ｍｏｔｉｖａｔｅｄｂｙｐｌａｕｓｉｂｌｅａｐｐｌｉｃａｔｉｏｎｓ…     

Existence and global attractivity of almost periodic solutions for a delayed differential neoclassical growth model

In this paper, we study a class of generalized differential neoclassical growth model with time‐varying delays, new criteria for the existence, and global attractivity of almost positive periodic solutions are established by using the theory of dichotomy and differential inequality techniques, together with constructing a suitable Lyapunov function. Finally, we present an example with numerical simulations to support the theoretical results. The obtained results are essentially new and complement previously known results. Copyright © 2016 John Wiley & Sons, Ltd.     

Global attractivity for scalar differential equations with small delay

For scalar functional differential equations , we refine the method of Yorke and 3/2-type conditions to prove the global attractivity of the trivial solution. The results are applied to establish sufficient conditions for the global attractivity of the positive equilibrium of scalar delayed population models of the form , and illustrated with the study of two food-limited population models with delay, for which several criteria for their global attractivity are given.     

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 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.     

Existence and global attractivity of positive periodic solution for a Volterra model with mutual interference and Beddington-DeAngelis functional response

In this paper, a Volterra model with mutual interference and Beddington-DeAngelis functional response is investigated, some sufficient conditions which guarantee the existence and global attractivity of positive periodic solution for the system are obtained. Furthermore, our results improve the main results of paper [1].     

Periodic solutions in periodic state-dependent delay equations and population models

Sufficient and realistic conditions are obtained for the existence of positive periodic solutions in periodic equations with state-dependent delay. The method involves the application of the coincidence degree theorem and estimations of uniform upper bounds on solutions. Applications of these results to some population models are presented. These application results indicate that seasonal effects on population models often lead to synchronous solutions. In addition, we may conclude that when both seasonality and time delay are present and deserve consideration, the seasonality is often the generating force for the often observed oscillatory behavior in population densities.

     

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.     

Global attractivity in delay “food-limited” models with exponential impulses

In this paper, we are concerned with the global attractivity of the positive equilibrium of the following delay “food-limited” model with exponential impulses: