具有功能性反应和时滞的扩散捕食-食饵系统

考虑具有功能性反应和时滞的扩散捕食-食饵系统，其中食饵连两个斑块间具有一定的扩散系数，捕食者可以两个斑块中任意走动，我们讨论了系统的一致持久性和周期解的存在性及全局吸引性．     

一类概周期时滞捕食-食饵系统的概周期解

本文讨论一类概周期时滞捕食－食饵系统的一致持久性,通过构造一个Ｌｉａｐｕｎｏｖ函数得到该系统有界解的唯一性,并且给出正概周期解的存在唯一性定理。     

具有脉冲效应的周期三种群捕食-食饵系统

本文讨论一类具有脉冲效应和周期系数的两个食饵一个捕食者的捕食-食饵系统的动力学行为.利用脉冲微分方程比较定理和乘子理论,证明了系统的有界性,讨论了平凡周期解和半平凡周期解的稳定性,利用重合度的理论给出了系统存在周期正解的充分条件.     

一类具有时滞和捕获的捕食食饵系统周期解的全局存在性

通过利用Mawhin重合度理论讨论了一类具有时滞和捕获的捕食食饵系统的全局周期解的存在性,得到了周期解存在的充分条件.     

一类具有阶段结构的非自治捕食-食饵系统的持久性与周期解

研究了一类具有阶段结构的非自治的捕食-食饵系统的渐近性质,得到了在适当条件下该系统的持久性,对应周期系统正周期解的存在性、唯一性以及全局渐近稳定性.     

一类带有无穷时滞的Lotka-Volterra食饵捕食系统的正周期解

首先给出了一类带有无穷时滞的Lotka-Volterra食饵捕食系统,接着使用Krasnoselskii’s不动点定理研究了其正周期解的存在性;然后证明了正周期解的全局吸引性;最后,给出了一个例子.     

具有时滞和基于比率的两种群捕食者-食饵扩散系统的周期解

本文研究了一类具有时滞和基于比率的两种群捕食者—食饵扩散系统，利用重合度理论建立了这类系统正周期解的存在性判据。     

Holling Ⅳ捕食-食饵时滞系统的多个周期解

应用重合度定理研究了一类具有Holling Ⅳ类功能性反应时滞捕食-食饵系统的周期解的存在性问题,建立了该系统具有至少两个正周期解的充分条件.     

Holling IV捕食-食饵时滞系统的多个周期解

应用重合度定理研究了一类具有Holling IV类功能性反应时滞捕食-食饵系统的周期解的存在性问题,建立了该系统具有至少两个正周期解的充分条件．     

具有时变时滞和Holling-N类功能反应的脉冲捕食系统的周期解

考虑具有时变时滞、Holling-N类功能反应和脉冲效应的捕食-食饵系统的数学模型.利用Mawhin重合度理论,并结合同伦不变性质,以及Young不等式,获得该系统正周期解存在的充分条件,推广和改进(正)最近一些文献的结果.     

具脉冲效应的时滞周期捕食与被捕食系统正周期解的存在性

本文研究一类具脉冲效应的时滞周期捕食与被捕食系统，利用重合度理论中的方法，获得该系统至少存在一个正周期解的充分条件。     

PERIODIC SOLUTIONS FOR GENERALIZED PREDATOR-PREY SYSTEMS WITH TIME DELAY AND DIFFUSION

A set of easily verifiable sufficient conditions are derived for the existence of positive periodic solutions for delayed generalized predator-prey dispersion system x'1 (t) = x1 (t)g1 (t, x1 (t) ) - a1 (t)y(t)p1 (x1 (t) ) D1 (t)(x2(t) - x1 (t) ),x'2 (t) = x2 (t)g2 (t, x2 (t) ) - a2 (t)y(t)p2 (x2 (t) ) D2(t)(x1 (t) - x2 (t)),y' (t) = y(t) {-h(t, y(t) ) b1 (t)p1 (x1 (t - τ1 ) ) b2(t)p2(x2(t - τ2))],where ai(t), bi(t) and Di(t)(i = 1, 2) are positive continuous T-periodic functions, gi(t, xi)(i = 1,2) and h(t,y) are continuous and T-periodic with respect to t and h(t,y) ＞ 0 for y ＞ 0, t, y ∈ R, pi(x)(i = 1, 2) are continuous and monotonously increasing functions, and pi(xi) ＞ 0 for xi ＞ 0.     

POSITIVE PERIODIC SOLUTION FOR TWO-SPECIES PREDATOR-PREY DIFFUSION-DELAY MODELS WITH FUNCTIONAL RESPONSE

In this paper, a two-species diffusive predator-prey model with time delay and functional response is studied, where all parameters are time dependent. By using the continuation theorem of coincidence degree theory, the existence of a positive periodic solution for this system is established.     

PERIODIC SOLUTION TO PREDATOR-PREY CHAIN SYSTEM WITH IMPULSIVE EFFECTS AND BEDDINGTON-DEANGELIS FUNCTIONAL RESPONSE

In this paper, a predator-prey chain system with impulsive effects and Beddington-DeAngelis functional response is studied. We investigate the existence of periodic solu-tion by coincidence degree theory. Sufficient conditions are obtained for the existence of periodic solution.     

POSITIVE PERIODIC SOLUTION OF A PREDATOR-PREY SYSTEM WITH TIME DELAY

By using continuation theorem in coincidence degree theory,we study the existence of positive periodic solution for a delay and mutual interference predator- prey system with functional response,and obtain sufficient conditions for the existence of positive periodic solution.     

GLOBAL EXISTENCE OF POSITIVE PERIODIC SOLUTION FOR A NEUTRAL DELAY COMPETITIVE SYSTEM

In this paper, by means of Mawhin's coincidence degree theory and somenew techniques, sufficient conditions for the global existence of positive periodicsolution to a class of neutral type competitive system with delays are obtained.     

具有偏差变元的捕食者-食饵系统全局周期解的存在性

利用重合度理论中的延拓定理讨论了一类具有偏差变元的捕食者-食饵系统全局周期解的存在性,得到了一些新结果。     

POSITIVE PERIODIC SOLUTION OF AN INTEGRO-DIFFERENTIAL PREDATOR-PREY SYSTEM WITH INFINITE DELAYS

With the help of a continuation theorem based on Gaines and Mawhin's coincidence degree, easily verifiable criteria are established for the global existence of positive periodic solutions of a differential-integral predator-prey system with infinite delaywhere N1(t), N2(t) satisfy N1(t) =φ1(t), N2(t) =φ2(t), φi∈ BC((∞,0],R+φi(0)> 0,i=1,2, ∫0+∞Ki(s)ds = 1, i=1,2,3.     

EXISTENCE OF POSITIVE PERIODIC SOLUTION FOR A DELAYED PERIODIC PREDATOR-PREY MODEL OF IVLEV TYPE

A periodic coefficients predator-prey system of Ivlev type with both discrete and continuous time delay is investigated. A sufficient condition of the existence of positive periodic solution is established for the system by using the continuation theorem of coincidence degree theory.     

周期捕食与被捕食系统正周期解的稳定性

本文研究具周期系数的Ｌｏｔｋａ－Ｖｏｌｔｅｒｒａ捕食与被捕食系统，建立了系统正周期解渐近稳定和全局稳定的新的判别准则。