共查询到19条相似文献,搜索用时 109 毫秒
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具有放牧率的n阶Lotka-Volterra概周期竞争系统 总被引:9,自引:0,他引:9
利用线性系统指数型二分性理论和不动点定理给出了具有放牧率的n阶Lotka-Volterra概周期系统,给出该系统存在唯一稳定的概周期正解的一个实用、简洁的充分条件. 相似文献
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具有放牧率的某些周期生态模型 总被引:5,自引:2,他引:3
§1.引言对生态数学中的logistic模型以及Lotka-Volterra模型的研究已从常系数转向变系数,例如,[1-3]讨论了周期系数的情形,[4]讨论了概周期系数的情形。文[8]指出,当这些模型具有放牧率时,尚待研究。本文所讨论的是有周期放牧率的几种周期模型。§2讨论有放牧率的logistic模型, 相似文献
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研究具有阶段结构的多种群竞争系统,得到该系统一致持久,正周期解全局渐近稳定及概周期解的存在性与一致渐近稳定性的充分条件。 相似文献
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利用不动点原理,给出了具有无穷时滞的生态竞争系统存在概周期解的简洁而实用的充分条件. 相似文献
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讨论了一类具有阶段结构和第Ⅱ类功能反应的三种群混合模型,其中捕食种群具有阶段结构.得到在适当的条件下系统的持续生存,对应周期系统正周期解的存在性、唯一性以及全局稳定性. 相似文献
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An equation of growth of a single species with realistic dependence on crowding and seasonal factors
Martino Bardi 《Journal of mathematical biology》1983,17(1):33-43
Various biological phenomena lead to single species models where the relative rate of increase is a non-monotone function of the density, i.e. depensation models. A brief survey of the literature and some new models are given. A nonlinear nonautonomous O.D.E. is proposed as a general depensation model in a periodically fluctuating environment. Results on existence, multiplicity and global stability of periodic solutions are given. 相似文献
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固定周期脉冲微分方程到状态依赖脉冲的转化及应用 总被引:1,自引:0,他引:1
本文研究了一类二维状态依赖脉冲微分方程的阶1周期解存在性和轨道稳定性条件.然后,将一维固定周期脉冲的微分方程转化为二维状态依赖脉冲微分方程,研究其阶一周期解的存在性和稳定性.作为应用,我们研究了固定周期常数收获的Logistic方程的动力学性质,以及两个固定周期注射药物单室扩散模型的动力学性质. 相似文献
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A class of population models is considered in which the parameters such as fecundity, mortality and interaction coefficients are assumed to be age-dependent. Conditions for the existence, stability and global attractivity of steady-state and periodic solutions are derived. The dependence of these solutions on the maturation periods is analyzed. These results are applied to specific single and multiple population models. It is shown that periodic solutions cannot occur in a general class of single population age-dependent models. Conditions are derived that determine whether increasing the maturation period has a stabilizing effect. In specific cases, it is shown that any number of switches in stability can occur as the maturation period is increased. An example is given of predator-prey model where each one of these stability switches corresponds to a stable steady state losing its stability via a Hopf bifurcation to a periodic solution and regaining its stability upon further increase of the maturation period. 相似文献
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Clustering behaviours have been found in numerous multi-strain transmission models. Numerical solutions of these models have shown that steady-states, periodic, or even chaotic motions can be self-organized into clusters. Such clustering behaviours are not a priori expected. It has been proposed that the cross-protection from multiple strains of pathogens is responsible for the clustering phenomenon. In this paper, we show that the steady-state clusterings in existing models can be analytically predicted. The clusterings occur via semi-simple double zero bifurcation from the quotient networks of the models and the patterns which follow can be predicted through the stability analysis of the bifurcation. We calculate the stability criteria for the clustering patterns and show that some patterns are inherently unstable. Finally, the biological implications of these results are discussed. 相似文献
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时变环境下Chemostat中微生物连续培养食物链模型的分歧分析 总被引:2,自引:0,他引:2
研究均匀搅拌的Chemostat中微生物连续培养的单食物链模型.模型的特点是在营养输入项中引入时变环境,以便更逼真地模拟自然现象.用单特征值分歧定理得到了周期解存在的条件,用Crandall-Rabinowitz定理证明了单种群分歧解的稳定性. 相似文献
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According to the economic and biological aspects of renewable resources management, we propose a Lotka–Volterra predator–prey model with state dependent impulsive harvest. By using the Poincaré map, some conditions for the existence and stability of positive periodic solution are obtained. Moreover, we show that there is no periodic solution with order larger than or equal to three under some conditions. Numerical results are carried out to illustrate the feasibility of our main results. The bifurcation diagrams of periodic solutions are obtained by using the numerical simulations, and it is shown that a chaotic solution is generated via a cascade of period-doubling bifurcations, which implies that the presence of pulses makes the dynamic behavior more complex. 相似文献
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Shihe Xu 《Journal of biological dynamics》2017,11(1):504-520
In this paper, the existence, uniqueness and exponential stability of almost periodic solutions for a mathematical model of tumour growth are studied. The establishment of the model is based on the reaction–diffusion dynamics and mass conservation law and is considered with a delay in the cell proliferation process. Using a fixed-point theorem in cones, the existence and uniqueness of almost periodic solutions for different parameter values of the model is proved. Moreover, by the Gronwall inequality, sufficient conditions are established for the exponential stability of the unique almost periodic solution. Results are illustrated by computer simulations. 相似文献