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讨论了具有相互干扰和密度制约的Ⅰ型功能反应下且食饵种群具有收获率的捕食系统模型,得到系统正平衡点的存在条件及全局稳定的一些结果. 相似文献
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具非线性饱和功能反应的捕食者-食饵系统的定性分析 总被引:1,自引:0,他引:1
研究了一类具有非线性饱和功能反应的捕食者—食饵系统的定性行为.结果表明:当正平衡点稳定时,系统为全局渐近稳定的;当正平衡点不稳定时,系统存在唯一稳定的极限环. 相似文献
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研究了一类食饵具有时滞和自食现象的捕食者-食饵征税系统,并在此基础上将税收考虑进去.通过控制税收量来保护资源不被过渡开发,并在适当的假设条件下,讨论了平衡点的存在性.采用RouthHurwitz判别法得到系统正平衡点局部渐近稳定性的条件,以及通过构造Lyapunov函数证明了系统正平衡点是全局渐近稳定的,同时利用Pontrjagin最大值原理给出了最优征税策略,得到了贴现率能够影响捕获种群的利润水平的结论,目的在于既能保护生态系统又能使经济收益达到最大.通过相应的特征方程,分析了时滞对系统的稳定性产生了影响,并得出了当时滞经过τ=τ_O时系统经历Hopf分支的结论. 相似文献
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General models of two predator-prey systems are considered in which the prey are linked through competition and the predators are not directly linked. The persistence criteria based upon a technique developed by Gard is obtained. In addition, a condition for the global asymptotic stability of the interior equilibrium is discussed. 相似文献
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《Journal of biological dynamics》2013,7(1):159-171
The present study deals with the analysis of a predator–prey like model consisting of system of differential equations with piecewise constant arguments. A solution of the system with piecewise constant arguments leads to a system of difference equations which is examined to study boundedness, local and global asymptotic behaviour of the positive solutions. Using Schur–Cohn criterion and a Lyapunov function, we derive sufficient conditions under which the positive equilibrium point is local and global asymptotically stable. Moreover, we show numerically that periodic solutions arise as a consequence of Neimark-Sacker bifurcation of a limit cycle. 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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One goal of this paper is to give an algorithm for computing a threshold condition for epidemiological systems arising from compartmental deterministic modeling. We calculate a threshold condition T(0) of the parameters of the system such that if T(0)<1 the disease-free equilibrium (DFE) is locally asymptotically stable (LAS), and if T(0)>1, the DFE is unstable. The second objective, by adding some reasonable assumptions, is to give, depending on the model, necessary and sufficient conditions for global asymptotic stability (GAS) of the DFE. In many cases, we can prove that a necessary and sufficient condition for the global asymptotic stability of the DFE is R(0)< or =1, where R(0) is the basic reproduction number [O. Diekmann, J.A. Heesterbeek, Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation, Wiley, New York, 2000]. To illustrate our results, we apply our techniques to examples taken from the literature. In these examples we improve the results already obtained for the GAS of the DFE. We show that our algorithm is relevant for high dimensional epidemiological models. 相似文献
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For the Levene model with soft selection in two demes, the maintenance of polymorphism at two diallelic loci is studied. Selection is nonepistatic and dominance is intermediate. Thus, there is directional selection in every deme and at every locus. We assume that selection is in opposite directions in the two demes because otherwise no polymorphism is possible. If at one locus there is no dominance, then a complete analysis of the dynamical and equilibrium properties is performed. In particular, a simple necessary and sufficient condition for the existence of an internal equilibrium and sufficient conditions for global asymptotic stability are obtained. These results are extended to deme-independent degree of dominance at one locus. A perturbation analysis establishes structural stability within the full parameter space. In the absence of genotype-environment interaction, which requires deme-independent dominance at both loci, nongeneric equilibrium behavior occurs, and the introduction of arbitrarily small genotype-environment interaction changes the equilibrium structure and may destroy stable polymorphism. The volume of the parameter space for which a (stable) two-locus polymorphism is maintained is computed numerically. It is investigated how this volume depends on the strength of selection and on the dominance relations. If the favorable allele is (partially) dominant in its deme, more than 20% of all parameter combinations lead to a globally asymptotically stable, fully polymorphic equilibrium. 相似文献
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具有变消耗率微生物连续培养模型的定性分析 总被引:1,自引:0,他引:1
研究了一类具有变消耗率的微生物连续培养系统,当消耗率是线性函数时得到了正平衡点全局渐近稳定的充要条件,当消耗率是二次函数时得到了系统存在极限环的充分条件,同时利用分支理论研究系统存在Hopf分支的条件,判定了极限环的稳定性. 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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In this paper, a new sufficient condition is given for the global asymptotic stability and global exponential output stability of a unique equilibrium points of delayed cellular neural networks (DCNNs) by using Lyapunov method. This condition imposes constraints on the feedback matrices and delayed feedback matrices of DCNNs and is independent of the delay. The obtained results extend and improve upon those in the earlier literature, and this condition is also less restrictive than those given in the earlier references. Two examples compared with the previous results in the literatures are presented and a simulation result is also given. 相似文献