Global positive periodic solutions of periodic n-species competition systems

In this paper, an easily verifiable necessary and sufficient condition for the existence of positive periodic solutions of generalized n-species Lotka-Volterra type and Gilpin-Ayala type competition systems is obtained. It improves a series of the well-known sufficiency theorems in the literature about the problems mentioned above. The method is based on a well-known fixed point theorem in a cone of Banach space. This approach can be applied to more general competition systems.     

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

     

On the existence of positive periodic solutions for neutral functional differential equation with multiple deviating arguments

By means of the abstract continuation theory for k-contractions, some criteria are established for the existence and nonexistence of positive periodic solutions of the following neutral functional differential equation:

     

Existence of positive periodic solution of n-dimensional Lotka-Volterra system with delays

With the help of a continuation theorem based on coincidence degree, easily verifiable criteria are established for the existence of positive periodic solutions of n-D Lotka-Volterra system with delays. And sufficient conditions are obtained for the persistence of the delay system. Finally, computer simulations are presented to illustrate the conclusions.     

Stable periodic solution of a discrete periodic Lotka-Volterra competition system

This paper discusses a discrete Lotka-Volterra competition system. We first obtain the persistence of the system. Assuming that the coefficients in the system are periodic, we obtain the existence of a periodic solution. Moreover, under some additional conditions, this periodic solution is globally stable. Our results not only reduce to those for the scalar equation when there is no coupling but also improve and complement some in the literature.     

Periodic solution of neutral Lotka-Volterra system with periodic delays

A nonautonomous n-species Lotka-Volterra system with neutral delays is investigated. A set of verifiable sufficient conditions is derived for the existence of at least one strictly positive periodic solution of this Lotka-Volterra system by applying an existence theorem and some analysis techniques, where the assumptions of the existence theorem are different from that of Gaines and Mawhin's continuation theorem [R.E. Gaines, J.L. Mawhin, Coincidence Degree and Nonlinear Differential Equations, Springer-Verlag, Berlin, 1977] and that of abstract continuation theory for k-set contraction [W. Petryshyn, Z. Yu, Existence theorem for periodic solutions of higher order nonlinear periodic boundary value problems, Nonlinear Anal. 6 (1982) 943-969]. Moreover, a problem proposed by Freedman and Wu [H.I. Freedman, J. Wu, Periodic solution of single species models with periodic delay, SIAM J. Math. Anal. 23 (1992) 689-701] is answered.     

具偏差变元的中立型微分方程正周期解的存在性

By means of an abstract continuation theorem, the existence criteria are established for the positive periodic solutions of a neutral functional differential equation dN/dt=N(t)[a(t)-β(t)N(t)-b(t)N(t-a(t))-c(t)N(t-τ(t))]     

非自治Kolmogorov竞争系统的严格正解

In this paper, the existence of strictly positive solutions for N species normutonomous Kolmogorov competition systems is studied. By applying the Schauder‘s flxed pointtheorem some new sufficient conditions are established. In particular, for the almost periodicsystem, tile existence of strictly positive almost periodic solutiorts is obtained, Some previousresults are improved and generalized.     

中立型时滞Lotka-Volterra系统正周期解的存在性

本文研究了具有m个捕食者n个食饵的中立型时滞Lotka-Volterra系统,并 利用重合度理论中的连续性引理,得到了该系统正周期解存在性的充分条件.     

Positive almost periodic solutions for a class of Liénard-type systems with multiple deviating arguments

This paper considers the Liénard-type systems with multiple deviating arguments. Sufficient conditions for the existence and exponential stability of positive almost periodic solutions are established, which are new and complement previously known results.     

An extension of kamake theorem and periodic lotka-volterra systems with diffusion

Based on an extended Kamake theorem, the global attractivity of a positive periodic solution for a Lotka-Volterra prey-predator periodic system with diffusion is given. This gives a partial answer to a problem of Hess.     

一类具多偏差变元的p-Laplacian方程周期解的存在性

研究了一类具多偏差变元的p-Laplacian方程,为了得到该方程周期解的先验估计,运用分析技巧建立了一些新的不等式,进而利用Mawhin连续定理得到了这类方程周期解的存在性,得到了一些新的结果,推广和改进了已有结果.     

具有时滞的周期Lotka-Volterra型系统的全局渐近稳定性

考虑一般具有时间依赖时滞和连续分布时滞的Ｎ－种群周期Ｌｏｔｋａ－Ｖｏｌｔｅｒｒａ型系统。通过使用Ｌｉａｐｕｎｏｖ函数方法得到了关于正周期解的存在性和全局渐近稳定性的充分条件。这些条件改进和推广了最近被Ｗａｎｇ,Ｃｈｅｎ,Ｌｕ「２」和Ａｈｌｉｐ,Ｋｉｎｇ「４」得到的相应结果。     

Global attractivity of periodic solution for neutral functional differential system with multiple deviating arguments

In this paper, a kind of neutral functional differential system with multiple deviating arguments is considered. By means of Mawhin's coincidence degree theory and Lyapunov method, a sufficient condition is obtained for guaranteeing the existence and global attractivity of periodic solution for the system. It is interesting that the result is related to the multiple deviating arguments τ_i(i = 1, 2, …, m). An example is given to show the feasibility of the result in the last section. Copyright © 2011 John Wiley & Sons, Ltd.     

Positive periodic solutions of nonautonomous functional differential systems

Considered is the periodic functional differential system with a parameter, x^′(t)=A(t,x(t))x(t)+λf(t,xt). Using the eigenvalue problems of completely continuous operators, we establish some criteria on the existence of positive periodic solutions. Moreover, we apply the results to a couple of population models and obtain sufficient conditions for the existence of positive periodic solutions, which are compared with existing ones.     

Nonautonomous Lotka-Volterra Systems with Delays

The paper studies the general nonautonomous Lotka-Volterra multispecies systems with finite delays. The ultimate boundedness, permanence, global attractivity, and existence and uniqueness of strictly positive solutions, positive periodic solutions, and almost periodic solutions are obtained. These results are basically an extension of the known results for nonautonomous Lotka-Volterra multispecies systems without delay to systems with delay.     

周期二维Lotka—Volterra系统的一些新结果

该文研究周期二维Lotka－Volterra捕食食饵系统解的有界性，持续生存性以及正周期解的存在性和全局稳定性．并将结果推广到食饵有补充的周期二维Lotka－Volterra竞争系统上去，得到了一系列新的结果，改进和推广了文[1—3]的主要结论．     

Positive periodic solutions of nonlinear differential systems with impulses

By using a fixed point theorem of strict-set-contraction, sufficient conditions for the existence of positive periodic solutions of nonlinear differential systems with impulses are obtained. As applications of our results, the existence of positive periodic solutions are established for delay Lotka–Volterra systems with impulses or without impulses.     

Existence of positive periodic solutions of first order neutral differential equations with variable coefficients

This work deals with the existence of positive $\omega$-periodic solutions for the first order neutral differential equation. The results are established using Krasnoselskii’s fixed point theorem. An example is given to support the theory.     

五种群Lotka-Volterra混合系统的全局渐近稳定性

考虑周期系数的五种群Lotka-Volterra模型,种群间既有捕食关系又有竞争关系,得到该系统的正周期解的存在性及全局渐近稳定性的条件.