| 具有时滞S型Holling功能性反应模型的Hopf分支 |
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| 引用本文： | 陈斯养,张艳.具有时滞S型Holling功能性反应模型的Hopf分支[J].西安石油大学学报(自然科学版),2012,27(1):104-110,123. |
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| 作者姓名： | 陈斯养 张艳 |
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| 作者单位： | 陕西师范大学数学与信息科学学院,陕西西安,710062 |
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| 摘 要： | 研究了一类具有离散时滞的Holling型功能反应生态系统的稳定性与Hopf分支问题.由特征值理论得到系统正平衡态局部渐近稳定的充分条件;以时滞τ为参数,得出系统存在Hopf分支的条件及分支附近周期解的稳定性;通过实例验证定理条件和结论的可实现性,利用Matlab软件绘出不同参数值的解曲线,并对图像进行对比分析.
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| 关 键 词： | 功能反应 Hopf分支 时滞 稳定性 |
Hopf bifurcation of a model with delay and Holling-S type functional response |
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| CHEN Si-yang,ZHANG Yan.Hopf bifurcation of a model with delay and Holling-S type functional response[J].Journal of Xian Shiyou University,2012,27(1):104-110,123. |
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| Authors: | CHEN Si-yang ZHANG Yan |
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| Institution: | (College of Mathematics and Information Science,Shaanxi Normal University,Xi’an 710062,Shaanxi,China) |
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| Abstract: | The stability and Hopf bifurcation of a class of ecological model with discrete delays and Holling type functional response are investigated.Sufficient conditions for the linear asymptotic stability of the positive equilibrium of the system are obtained by using the theory of characteristic value.The conditions for Hopf bifurcation existence and the stability of the bifurcation periodic solution are discussed by regarding the delay as a parameter.The previous theorems and conclusions are verified by some examples.The solution curves about various parameters are achieved by Matlab.The different figures are compared and analyzed. |
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| Keywords: | functional response Hopf bifurcation delay stability |
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