时滞Lotka-Volterra竞争型系统的概周期解

研究具有离散时滞的N-种群Lotka-Volterra竞争型系统，得到了系统存在唯一性概周期解的一组充分条件。     

The criteria of ultimate boundedness for nonautonomous Lotka-Volterra tree systems

In this paper, by introducing a concept called the degree of species, we obtain a set of sufficient conditions for the ultimate boundedness of nonautonomous n-species Lotka-Volterra tree systems. As a consequence, we also obtain the criteria of the existence of a globally stable equilibrium point for the autonomous Lotka-Volterra tree system. The criteria in this paper are in explicit forms of the parameters, and thus, are easily verifiable.     

一类多偏差变元的n种群Lotka-Volterra模型的周期正解

本文研究了一类多偏差变元Lotka-Volterra种群模型的间期正解问题,利用重合度拓展定理和一些分析技巧,得到了周期正解存在性的新结果.与已有文献相比,本文所讨论的模型更具一般性,它包含了以前人们所研究的竞争-种群模型、捕食-种群模型等,而且估计先验界的方法也是全新的.     

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．     

On the long time behavior of non-autonomous Lotka-Volterra models with diffusion via the sub-supertrajectory method

In this paper we study in detail the geometrical structure of global pullback and forwards attractors associated to non-autonomous Lotka-Volterra systems in all the three cases of competition, symbiosis or prey-predator. In particular, under some conditions on the parameters, we prove the existence of a unique nondegenerate global solution for these models, which attracts any other complete bounded trajectory. Thus, we generalize the existence of a unique strictly positive stable (stationary) solution from the autonomous case and we extend to Lotka-Volterra systems the result for scalar logistic equations. To this end we present the sub-supertrajectory tool as a generalization of the now classical sub-supersolution method. In particular, we also conclude pullback and forwards permanence for the above models.     

Permanence for a delayed periodic predator-prey model with prey dispersal in multi-patches and predator density-independent

In this paper, we study two species time-delayed predator-prey Lotka-Volterra type dispersal systems with periodic coefficients, in which the prey species can disperse among n patches, while the density-independent predator species is confined to one of patches and cannot disperse. Sufficient conditions on the boundedness, permanence and existence of positive periodic solution for this systems are established. The theoretical results are confirmed by a special example and numerical simulations.     

Global asymptotic stability of Lotka-Volterra 3-species reaction-diffusion systems with time delays

This paper is concerned with three 3-species time-delayed Lotka-Volterra reaction-diffusion systems and their corresponding ordinary differential systems without diffusion. The time delays may be discrete or continuous, and the boundary conditions for the reaction-diffusion systems are of Neumann type. The goal of the paper is to obtain some simple and easily verifiable conditions for the existence and global asymptotic stability of a positive steady-state solution for each of the three model problems. These conditions involve only the reaction rate constants and are independent of the diffusion effect and time delays. The result of global asymptotic stability implies that each of the three model systems coexists, is permanent, and the trivial and all semitrivial solutions are unstable. Our approach to the problem is based on the method of upper and lower solutions for a more general reaction-diffusion system which gives a common framework for the 3-species model problems. Some global stability results for the 2-species competition and prey-predator reaction-diffusion systems are included in the discussion.     

Traveling wave solutions in delayed reaction-diffusion systems with mixed monotonicity

This paper deals with the existence of traveling wave solutions in delayed reaction-diffusion systems with mixed monotonicity. Based on two different mixed-quasi monotonicity reaction terms, we propose new conditions on the reaction terms and new definitions of upper and lower solutions. By using Schauder’s fixed point theorem and a new cross-iteration scheme, we reduce the existence of traveling wave solutions to the existence of a pair of upper and lower solutions. The general results obtained have been applied to type-K monotone and type-K competitive diffusive Lotka-Volterra systems.     

Positive periodic solution of a more realistic three-species Lotka-Volterra model with delay and density regulation

In the paper, a more realistic three-species ratio-dependent Lotka-Volterra model with delay and diffusive and density regulation is investigated. By mean of the powerful and effective coincidence degree theory, we establish sufficient conditions for the existence of at least one positive periodic solution of the model. What’s more, the conditions are easily verifiable.     

Periodicity and stability for a Lotka-Volterra type competition system with feedback controls and deviating arguments

This paper deals with the general periodic Lotka-Volterra type competition systems with feedback controls and deviating arguments. By employing fixed point index theory on cone, an explicit necessary and sufficient condition for the global existence of the positive periodic solution of the systems is proved. By constructing a suitable Lyapunov functional, a set of easily verifiable sufficient conditions for the global asymptotic stability of the positive periodic solution of the systems is given.     

The Center Conditions and Hopf Cyclicity for a 3D Lotka-Volterra System

The main objective of this paper is not only to find necessary and The main objective of this paper is not only to find necessary and sufficient conditions for the existence of a center on a local center manifold for a three dimensional Lotka-Volterra system, but also to determine the maximum number of limit cycles that can bifurcate from the positive equilibrium as a fine focus. Firstly, the singular point quantities are computed and simplified to obtain necessary conditions for local integrability, and Darboux method is applied to show the sufficiency. Then, the Hopf bifurcation on the center manifold is investigated, from this, the conclusion of at most five small limit cycles generated in the vicinity of the equilibrium is obtained. To the best of our knowledge, this is the first case with five possible limit cycles for the cyclicity of 3D Lotka-Volterra systems.     

两种群非自治Lotka-Volterra竞争扩散系统的概周期解

本文讨论两种群概周期竞争扩散系统，利用微分不等式，证明了系统概周期解的存在、唯一性及其在壳扰动下的稳定性．     

非线性三种群空间周期解的存在性

本文考虑以下系统: ,用Darboux方 法彻底解决了该系统空间周期解的存在性问题.     

一类无穷时滞周期Lotka-Volterra型系统的正周期解

该文研究一类无穷时滞周期Ｌｏｔｋａ Ｖｏｌｔｅｒｒａ型系统正周期解的存在性．应用Ｓｃｈａｕｄｅｒ不动 点定理得到了一个比较一般的正周期解存在定理．文献［１,２］中的主要结果被改进和推广．     

n阶Lotka-Volterra系统永久持续生存的新判据(英文)

本文首先研究了n阶Lotka Volterra系统的非负平衡点之间的关系 .然后在此基础上研究了该系统的永久持续生存问题 ,得到了若干判别n阶Lotka Volterra系统永久持续生存的充要条件 .     

Integrability and linearizability of the Lotka-Volterra systems

Integrability and linearizability of the Lotka-Volterra systems are studied. We prove sufficient conditions for integrable but not linearizable systems for any rational resonance ratio. We give new sufficient conditions for linearizable Lotka-Volterra systems. Sufficient conditions for integrable Lotka-Volterra systems with 3:−q resonance are given. In the particular cases of 3:−5 and 3:−4 resonances, necessary and sufficient conditions for integrable systems are given.     

Lotka-Volterra equations in three dimensions satisfying the Kowalevski-Painlevé property

We examine a class of Lotka-Volterra equations in three dimensions which satisfy the Kowalevski-Painlevé property. We restrict our attention to Lotka-Volterra systems defined by a skew symmetric matrix. We obtain a complete classification of such systems. The classification is obtained using Painlevé analysis and more specifically by the use of Kowalevski exponents. The imposition of certain integrality conditions on the Kowalevski exponents gives necessary conditions. We also show that the conditions are sufficient.     

周期捕食被捕食系统正周期解存在的充要条件

研究周期环境下的Lotka-Volterra捕食被捕食系统。采用分歧理论和微分不等式方法,建立了关于正周期解存在的一个充分必要判别准则,总结和推广了文[1—4]中的主要结果。     

无穷时滞Lotka-Volterra型系统的正周期解

利用Schauder不动点定理讨论Lotka-Volterra型系统的正周期解存在性,得到了正周期解存在的充分条件.推广并改进了已有的结果.