| 一类具有连续和离散时滞的干扰模型的定性分析 |
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| 引用本文： | 左晓虹,陈斯养.一类具有连续和离散时滞的干扰模型的定性分析[J].云南师范大学学报(自然科学版),2009,29(4):16-21. |
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| 作者姓名： | 左晓虹 陈斯养 |
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| 作者单位： | 1. 陕西师范大学数学与信息科学学院,陕西,西安,710062;延安大学西安创新学院理工系,陕西,西安,710100
2. 陕西师范大学数学与信息科学学院,陕西,西安,710062 |
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| 基金项目： | 国家自然科学基金，国家自然科学基金 |
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| 摘 要： | 研究了一类具有连续时滞与离散时滞的单种群干扰模型的稳定性与Hopf分支问题。首先利用特征值理论得到平衡态局部渐近稳定的充要条件；再以时滞τ为参数，给出了Hopf分支的存在性及分支值处模型平衡态的稳定性的条件；最后举例验证了定理的条件和结论的可实现性，利用Madab得到其参数取不同数值时的曲线拟合图。
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| 关 键 词： | 时滞 Hopf分支 稳定性 |
Qualitative Analysis in a Class of Continuous and Discrete Time-delay Model with Interference |
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| ZUO Xiao-hong,CHEN Si-yang.Qualitative Analysis in a Class of Continuous and Discrete Time-delay Model with Interference[J].Journal of Yunnan Normal University (Natural Sciences Edition),2009,29(4):16-21. |
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| Authors: | ZUO Xiao-hong CHEN Si-yang |
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| Institution: | ZUO Xiao - hong, CHEN Si - yang ( 1. College of Mathematics and Information Science, Shaanxi Normal University, Xi＇an 710062, China; 2. Department of Science and Technology, Xi＇an Creation college of Ya＇an University, Xi＇an 710100, China) |
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| Abstract: | The stability and Hopf bifurcation for a class of ecological model with continuous and discrete delays of interference are investigated. Sufficient and necessary conditions of the asymptotically stability are obtained by using the theory of characteristic value. Furthermore, regarding the delay τ as a parameter, given conditions of the existence of Hopf bifurcation and the stability of model at τo . Finally, some examples together with their numerical simulations show the feasibility of our main resulte, Fitting maps about various parameters with their value are presented by using Matlab. |
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| Keywords: | Delay Hopf bifurcation stability |
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