| 一类非线性时滞微分方程模型系统的稳定性和Hopf分支分析 |
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| 引用本文： | 刘华祥,曾广洪,吴庆初. 一类非线性时滞微分方程模型系统的稳定性和Hopf分支分析[J]. 江西师范大学学报(自然科学版), 2009, 33(3) |
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| 作者姓名： | 刘华祥 曾广洪 吴庆初 |
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| 作者单位： | 广东海洋大学,理学院数学系,广东,湛江,524088;江西师范大学,数学与信息科学学院,江西,南昌,330022 |
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| 基金项目： | 广东海洋大学科研项目，江西师范大学青年成长基金 |
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| 摘 要： | 探讨了2个具有竞争相克作用的浮游植物种群的二维非线性时滞微分方程模型.分析了当离散时滞在临界值附近变动时,无时滞和有时滞系统的共生平衡点由局部渐近稳定变为不稳定.应用Hopf分支理论得出了分支周期解的存在条件,揭示了时滞T分支参数对系统基本动力学性质的影响.对所得的结果进行了数值模拟和可视化验证.通过选择适当的时滞参数值,所建立的时滞微分方程模型能够捕捉到各种浮游植物物种通常所展示的周期性暴发的振荡特性,这对于有害浮游植物的预防和控制具有一定的指导意义.
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| 关 键 词： | 浮游植物 时滞 Hopf分支 数值模拟 |
Stability and Hopf Bifurcation Analysis for a Nonlinear Differential Equation Model System with Time Delay |
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| LIU Hua-xiang,ZENG Guang-hong,WU Qing-chu. Stability and Hopf Bifurcation Analysis for a Nonlinear Differential Equation Model System with Time Delay[J]. Journal of Jiangxi Normal University (Natural Sciences Edition), 2009, 33(3) |
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| Authors: | LIU Hua-xiang ZENG Guang-hong WU Qing-chu |
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| Affiliation: | 1.Department of Mathematics;Guangdong Ocean University;Zhanjiang Guangdong 524088;China;2.Institute of Mathematics and Informatics;Jiangxi Normal University;Nanchang 330022;China |
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| Abstract: | A nonlinear two-dimensional time-delayed differential equation model system for two competitive phytoplankton species is considered.Firstly the local stability of positive equilibrium point for the non-delayed model system is discussed.Then local stability of positive equilibrium point and Hopf-Bifurcation analysis for the delayed model system is analysed by using Hopf-Bifurcation theory.Local Hopf-Bifurcation is existed as the time delay exceed a threshold value.Finally numerical simulations are carried ou... |
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| Keywords: | phytoplankton time delay Hopf-Bifurcation numerical simulation |
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