一类具离散和分布时滞的捕食–食饵模型的稳定性
Stability in a Predator-Prey Model with Discrete and Distributed Delays
DOI: 10.12677/AAM.2014.33022, PDF, HTML, 下载: 2,729  浏览: 5,974  科研立项经费支持
作者: 朱焕桃, 张钟德, 陈五立：湖南信息职业技术学院，长沙
关键词: 时滞；捕食模型；稳定性；Hopf分支；Delays； Predator Model； Stability； Hopf Bifurcation
摘要: 研究了一类具有离散和分布时滞的捕食–食饵模型系统，通过在正平衡点处线性化模型，并分析相应的特征方程，得到了正平衡点的渐近稳定性和模型产生Hopf分支的条件。
Abstract: The stability in a predator-prey model with discrete and distributed delays is investigated. By using linearized methods for the positive equilibrium and analyzing the corresponding characteristic equations, sufficient conditions for asymptotic stability of the positive equilibrium and the Hopf bifurcation occurring are derived.
文章引用：朱焕桃, 张钟德, 陈五立. 一类具离散和分布时滞的捕食–食饵模型的稳定性[J]. 应用数学进展, 2014, 3(3): 149-154. http://dx.doi.org/10.12677/AAM.2014.33022

参考文献

[1] Volterra, V. (1931) Lecons sur la theorie mathematique de la lutte pour la vie. Gauthier-Villars, Pairs.
[2] Brelot, M. (1931) Sur le probleme biologique hereditaiar de deux especes devorante et devore. Annali di Matematica Pura ed Applicata, 9, 58-74.
[3] Song, Y.L. and Yuan, S.L. (2006) Bifurcation analysis in a predator-prey system with time delay. Nonlinear Analysis: Real World Applications, 7, 265-284.
[4] 廖晓昕 (2001) 稳定性的数学理论及应用. 第二版, 华中师范大学出版社, 武汉.
[5] 马知恩, 周义仓 (2001) 常微分方程定性与稳定性方法. 科学出版社, 北京.
[6] Ruan, S.G. and Wei, J.J. (2003) On the zeros of transcendental functions with applications to stability of delay differential equations with two delays. Dynamics of Continuous, Discrete and Impulsive Systems, Ser. A: Ma-thematical Analysis, 10, 863-874.
[7] Hale, J.K. and Lunel, S.M.V. (1993) Introduction to Functional Differential Equations. Springer-Verlag, Berlin.

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