共查询到20条相似文献,搜索用时 78 毫秒
1.
研究了具有时滞的捕食与被捕食系统,分析了系统的正不变集、边界平衡点性质、全局渐近稳定性和持久生存性.当时滞(?)很小时,系统在正平衡点是局部渐近稳定的,当(?)从0增到(?)_0时,系统在正平衡点附近产生Hopf分支. 相似文献
2.
3.
4.
5.
研究了离散型二维竞争系统的渐近稳定性,得到了这类生物模型关于正平衡点渐近稳定的一系列充分条件。 相似文献
6.
建立并讨论了一类具有潜伏期、抗体免疫反应和CTL免疫反应的Holling II型发生率病毒动力学模型.定义了决定这个模型动力学性质的五个阈值,借助适当的Lyapunov函数得到:当R_(01)≤1时,无病平衡点全局渐近稳定,病毒被清除;当R_(01)1,R_(02)≤1,R_(03)≤1时,无免疫平衡点全局渐近稳定;当R_(02)1,R_(04)≤1时,CTL免疫主导平衡点全局渐近稳定;当R_(03)〉1,R_(04)≤1时,抗体免疫主导平衡点全局渐近稳定;当R_(04)1,R′_(04)1时,正平衡点全局渐近稳定. 相似文献
7.
讨论了区间多种群Volterra生态系统正平衡点的全局渐近稳定性,对于互惠型区间多种群Volterra生态系统不仅给出了正平衡点的全局稳定的充分必要条件,而且给出了系统存在平衡点的充分条件,对于一般的区间多种群Volterra生态系统给出了正平衡点全局稳定的充分条件。 相似文献
8.
9.
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
10.
11.
具有年龄结构的接种流行病模型正平衡解的全局稳定性 总被引:1,自引:0,他引:1
研究一个具有年龄结构的接种SIS流行病模型正平衡解的稳定性,先利用等价积分方程给出了正平衡解存在的充分条件,再利用迭代方法及函数的单调性,得到了零平衡解与正平衡解全局稳定的充分条件。 相似文献
12.
This paper presents a resource-dependent viability selection differential equation model of continuously reproducing diploid population with two alleles at one locus for a single limiting resource. This model assumes that the genotypic fitness is only a function of the limiting resource. The conditions that the interior equilibrium point of the system exists are that the heterozygote fitness is positive and the homozygote fitness is negative, or the heterozygote fitness is negative and the homozygote fitness is positive at the point. The sufficient and necessary conditions of locally asymptotical stability of the interior equilibrium point are that the heterozygote fitness is positive at the point, or the locally asymptotically stable equilibrium corresponds to the point at which the level of the limiting resource is locally minimized on the zero mean fitness curve, f = 0. 相似文献
13.
The main purpose of this paper is to develop criteria for which a simple food-chain model of intermediate type and of arbitrary length has a globally stable positive equilibrium and to develop criteria under which such a food chain exhibits uniform persistence. The same techniques are used to obtain conditions for a model of a predator-prey system with mutual interference of the predator to possess a globally stable positive equilibrium. 相似文献
14.
建立了一类含分布时滞的革新传播模型dU(t)/dt=-(α+βA(t))U(t)-pU(t)+p,dA(t)/dt=∫+∞ 0 αE(τ)U(t-τ)dτ+βU(t)A(t)-(p+k)A(t)。研究了分布时滞对传播过程的影响,讨论了正平衡点的存在性和唯一性及其局部与全局的渐近稳定性,当分布时滞的核函数取δe^-δτ时,证明了正平衡点是绝对渐近稳定的。 相似文献
15.
具有功能性反应的捕食与被捕食模型具有非常复杂的动态性质.特别是在常数收获下,该模型呈现了各种各样、纷杂多变的动态特性。其中包括正平衡点及其稳定性的变化、各种分叉的产生以及周期解和极限环的出现.本文重点研究了常数收获项对一类功能性反应模型的动态性能的影响,得到了该收获模型存在稳定正平衡点、产生分叉以及在Hopf分叉附近产生周期解和极限环的若干充分条件. 相似文献
16.
Xiaodong Lin 《Journal of mathematical biology》1991,29(8):779-790
In this paper, we examine an HIV/AIDS transmission model which has been widely used for studying the spread of HIV/AIDS through sexual contact. Some sufficient conditions are obtained for the uniqueness of endemic equilibrium. We also present a two-group model whose no-disease equilibrium is unstable but it has at least three positive endemic equilibria. 相似文献
17.
X Lin 《Mathematical biosciences》1991,104(1):111-134
In 1988, a multiple-group model for HIV transmission with preferred mixing was proposed by Jacquez and coworkers. In the present paper, the work done by Jacquez et al. is extended. It is shown that the stability modulus of the Jacobian matrix at the no-disease equilibrium is a threshold for this model. Furthermore, if the no-disease equilibrium is unstable, the number of infected individuals will remain above a certain positive level regardless of initial levels; that is, the disease will persist uniformly. The stability of the endemic equilibrium in the case of restricted mixing is also studied. A series of sufficient conditions for local and global asymptotic stability of the endemic equilibrium are stated. 相似文献
18.
Stoichiometric food quality and herbivore dynamics 总被引:4,自引:1,他引:3
Erik B. Muller Roger M. Nisbet Sebastiaan A. L. M. Kooijman James J. Elser & Edward McCauley 《Ecology letters》2001,4(6):519-529
Herbivores may grow with nutrient or energy limitation, depending on food abundance and the chemical composition of their food. We present a model that describes herbivore growth as a continuous function of two limiting factors. This function uses the synthesizing unit concept, has the hyperbolic Monod model as a limiting case, and has the same number of parameters as the Monod model coupled to Liebig's discontinuous minimum rule. We use the model to explore nutrient-limited herbivore growth in a closed system with algae, Daphnia and phosphorus as the limiting nutrient. Phosphorus in algae may substantially influence Daphnia growth. This influence changes over time and is most pronounced when algae and Daphnia populations fluctuate strongly. Relative to classic models that only consider food quantity as a determinant of Daphnia growth, our model shows richer dynamical behaviour. In addition to the standard positive equilibrium, which may be stable or unstable depending on nutrient availability, a new positive equilibrium may arise in our model when mortality rates are relatively high. This equilibrium is unstable and reduces the likelihood of long-term persistence of Daphnia in the system. 相似文献
19.
A hierarchically structured population model with a dependence of the vital rates on a function of the population density
(environment) is considered. The existence, uniqueness and the asymptotic behaviour of the solutions is obtained transforming the original
non-local PDE of the model into a local one. Under natural conditions, the global asymptotical stability of a nontrivial equilibrium
is proved. Finally, if the environment is a function of the biomass distribution, the existence of a positive total biomass
equilibrium without a nontrivial population equilibrium is shown.
Received 16 February 1996; received in revised form 16 September 1996 相似文献
20.
具有三个年龄阶段的单种群自食模型 总被引:5,自引:1,他引:4
建立并研究了两个具有三个年龄阶段的单种群自食模型.这篇文章的主要目的是研究时滞对种群生长的作用,对于没有时滞的的模型,我们利用Liapunov函数,得到了系统平衡点全局渐近稳定的充分条件;而具有时滞的的模型,我们得到,随着时滞T增加,当系数满足一定条件时,正平衡点的稳定性可以改变有限次,最后变成不稳定;否则,时滞模型的正平衡点的稳定性不改变。 相似文献