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1.
一个稀疏效应下的Volterra系统的极限环 总被引:16,自引:0,他引:16
应用数学生态学和微分方程定性理论,讨论了一个稀疏效应下的Volterra系统,在给定参数满足一定的条件下,证明了该系统极限环的存在性和唯一性,以及该系统的正平衡点全局渐近稳定。 相似文献
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本文讨论了一类具有强连续时滞的捕食-被捕食模型,分析了各非负平衡点的稳定性,利用区域连续收缩方法,得出非负平衡点全局稳定的充分条件,给出正平衡点全局稳定的充分条件,并给出系统出现Hopf的分支值. 相似文献
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捕食者有病的生态-流行病模型的分析 总被引:11,自引:1,他引:10
建立并分析了捕食者具有疾病且有功能反应的生态-流行病(SI)模型,讨论了解的有界性.应用特征根法得到了平衡点局部渐近稳定的充分条件,进一步分析了平衡点的全局稳定性,得到了边界平衡点和正平衡点全局稳定的充分条件。 相似文献
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三种群合作系统的全局渐近性态 总被引:2,自引:0,他引:2
考虑三种群合作系统:dχi/dt=χi(b-∑j3=1αijχj),χi(0)>0,b>0,αij<0,i≠j,i,j=1,2,3,完整地分析了其全局渐近性态:证明了该系统不存在闭轨,给出了正平衡点存在且全局渐近稳定的充要条件,证明了若系统不存在正平衡点,则所有解均趋于无穷. 相似文献
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本文研究离散单种扩散模型全局渐近稳定性,利用单调算子和凹算子的理论讨论了其全局渐近稳定性,并得到了正平衡点全局渐的稳定和物种绝灭的充分条件。 相似文献
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本文讨论了三种竞争种群的古典GLV系统.对系统所有非负平衡点的稳定性,进行了分析,给出了正平衡点全局稳定的充分条件,应用Hopf分支定理,我们给出了系统具有分支值的充分条件. 相似文献
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变时滞SIS流行病模型的稳定性分析 总被引:1,自引:1,他引:0
研究了一类时滞SIS流行病模型,分析了该模型无病平衡点和地方平衡点的存在性,得到了无病平衡点全局指数渐近稳定和地方病平衡点局部指数渐近稳定的充分条件,同时给出了地方病平衡点吸引区域的估计。 相似文献
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We introduce a graphical approach in the study of the qualitative behavior ofm species predator-prey systems. We prove that tree graphs imply global stability for Volterra models and local stability for
general models; furthermore, we derive sufficient conditions so that loop graphs imply stability and boundedness of the solutions. 相似文献
12.
《Journal of biological dynamics》2013,7(6):619-635
In this paper, the existence and global asymptotic stability of positive periodic solutions of periodic n-species Lotka–Volterra impulsive systems with several deviating arguments are studied. By using the continuation theorem of coincidence degree theory and Lyapunov–Razumikhin method, sufficient conditions are obtained. Some known results are improved and generalized. 相似文献
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We provide a global analysis of systems of within-host parasitic infections. The systems studied have parallel classes of different length of latently infected target cells. These systems can also be thought as systems arising from within-host parasitic systems with distributed continuous delays. We compute the basic reproduction ratio R0 for the systems under consideration. If R0< or =1 the parasite is cleared, if R0>1 and if a sufficient condition is satisfied we conclude to the global asymptotic stability (GAS) of the endemic equilibrium. For some generic class of models this condition reduces to R0>1. These results make possible to revisit some parasitic models including intracellular delays and to study their global stability. 相似文献
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A sufficient condition for the existence of a globally asymptotically stable equilibrium in Volterra models with continuous time delay is obtained, and some properties of the stable equilibrium are proven. Furthermore, some applications in which asymptotic stability only depends on the sign of the coefficients are considered. 相似文献
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The permanence and global attractivity for two-species difference systems of Lotka–Volterra type are considered. It is proved
that a cooperative system cannot be permanent. For a permanent competitive system, the explicit expression of the permanent
set E is obtained and sufficient conditions are given to guarantee the global attractivity of the positive equilibrium of the system.
Received: 21 May 1997 / Revised version: 25 November 1998 相似文献
16.
A complete classification for the global dynamics of a Lotka–Volterra two species competition model with seasonal succession is obtained via the stability analysis of equilibria and the theory of monotone dynamical systems. The effects of two death rates in the bad season and the proportion of the good season on the competition outcomes are also discussed. 相似文献
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Nishan Krikorian 《Journal of mathematical biology》1979,7(2):117-132
Summary The classical Volterra equations modelling three species predatorprey interactions are considered with the intention of developing global properties of their solutions. Thirty-four different cases are exhibited. Global asymptotic stability is established for all non-loop cases. Global boundedness is established for all but one kind of loop case, and a condition is exhibited which insures boundedness for that case also. Finally a particular case is shown to have unbounded solutions. 相似文献
18.
Global stability of population models 总被引:2,自引:0,他引:2
Paul Cull 《Bulletin of mathematical biology》1981,43(1):47-58
Local stability seems to imply global stability for population models. To investigate this claim, we formally define apopulation model. This definition seems to include the one-dimensional discrete models now in use. We derive a necessary and sufficient condition
for the global stability of our defined class of models. We derive an easily testable sufficient condition for local stability
to imply global stability. We also show that if a discrete model is majorized by one of these stable population models, then
the discrete model is globally stable. We demonstrate the utility of these theorems by using them to prove that the regions
of local and global stability coincide for six models from the literature. We close by arguing that these theorems give a
method for demonstrating global stability that is simpler and easier to apply than the usual method of Liapunov functions. 相似文献
19.
The theory of optimal foraging predicts abrupt changes in consumer behavior which lead to discontinuities in the functional
response. Therefore population dynamical models with optimal foraging behavior can be appropriately described by differential
equations with discontinuous right-hand sides. In this paper we analyze the behavior of three different Lotka–Volterra predator–prey
systems with optimal foraging behavior. We examine a predator–prey model with alternative food, a two-patch model with mobile
predators and resident prey, and a two-patch model with both predators and prey mobile. We show that in the studied examples,
optimal foraging behavior changes the neutral stability intrinsic to Lotka–Volterra systems to the existence of a bounded
global attractor. The analysis is based on the construction and use of appropriate Lyapunov functions for models described
by discontinuous differential equations.
Received: 23 March 1999 相似文献
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Stability criteria have recently been developed for coevolutionary Lotka–Volterra systems where individual fitness functions are assumed to be linear in the population state. We extend these criteria as part of a general theory of coevolution (that combines effects of ecology and evolution) based on arbitrary (i.e. nonlinear) fitness functions and a finite number of individual phenotypes. The central role of the stationary density surface where species’ densities are at equilibrium is emphasized. In particular, for monomorphic resident systems, it is shown coevolutionary stability is equivalent to ecological stability combined with evolutionary stability on the stationary density surface. Also discussed is how our theory relates to recent treatments of phenotypic coevolution via adaptive dynamics when there is a continuum of individual phenotypes. 相似文献