具有饱和与竞争项的捕食系统的全局分歧及稳定性

冯孝周;吴建华

系统科学与数学 ›› 2010, Vol. 30 ›› Issue (7) : 979-989.

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中国科学院数学与系统科学研究院期刊网
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系统科学与数学 ›› 2010, Vol. 30 ›› Issue (7) : 979-989. DOI: 10.12341/jssms09014
论文

具有饱和与竞争项的捕食系统的全局分歧及稳定性

    冯孝周(1), 吴建华(2)
作者信息 +

Global Bifurcation and Stability for Prey-Predator Model with Predator Saturation and Competition

    FENG Xiaozhou(1), WU Jianhua(2)
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摘要

利用比较原理,分歧理论,特征值线性扰动理论,主要研究了一类具有饱和与竞争反应项的捕食-食饵系统在Dirichlet边界条件下的平衡态分歧解.首先给出了一个先验估计和局部分歧解存在的充分条件.
然后对局部分歧解进行了全局延拓,得到了该系统平衡态的全局分歧解及其走向.最后讨论了局部分歧解的稳定性.

Abstract

In this paper, by maximum principle, eigenvalue perturbation principle and bifurcation theory, the bifurcation solution for prey-predator system with predator saturation and competition under the homogeneous Dirichlet boundary condition is studied. The local bifurcation solution and its stability, the global bifurcation solution and its behaviour are obtained.

关键词

捕食-食饵系统 / 分歧解 / 稳定性.

Key words

Prey-predator system / bifurcation solution / stability.

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冯孝周 , 吴建华. 具有饱和与竞争项的捕食系统的全局分歧及稳定性. 系统科学与数学, 2010, 30(7): 979-989. https://doi.org/10.12341/jssms09014
FENG Xiaozhou , WU Jianhua. Global Bifurcation and Stability for Prey-Predator Model with Predator Saturation and Competition. Journal of Systems Science and Mathematical Sciences, 2010, 30(7): 979-989 https://doi.org/10.12341/jssms09014
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