| 一类带有竞争和自反时滞的网站竞争系统的Hopf分支 |
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| 引用本文： | 张金龙,窦霁虹,石雁.一类带有竞争和自反时滞的网站竞争系统的Hopf分支[J].纯粹数学与应用数学,2011,27(1):51-55. |
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| 作者姓名： | 张金龙 窦霁虹 石雁 |
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| 作者单位： | 西北大学数学系,陕西,西安,710127 |
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| 摘 要： | 不同于以往研究网站竞争系统时,仅考虑带有自反时滞或竞争时滞的情况,本文研究了一类同时带有竞争时滞和自反时滞的网站竞争系统,并以时滞作为分支参数,通过分析正平衡点处的特征方程,研究了正平衡点的稳定性,证明了Hopf分支的存在性,得到了发生Hopf分支时的临界的时滞值,最后通过数值模拟进一步验证了所得结论.
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| 关 键 词： | 竞争时滞 自反时滞 网站系统 Hopf分支 |
Hopf bifurcation of a competitive web-site system with reflexive and competition delays |
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| ZHANG Jin-long,DOU Ji-hong,SHI Yan.Hopf bifurcation of a competitive web-site system with reflexive and competition delays[J].Pure and Applied Mathematics,2011,27(1):51-55. |
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| Authors: | ZHANG Jin-long DOU Ji-hong SHI Yan |
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| Institution: | (Department of Mathematics, Northwest University, Xi＇an 710127, China) |
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| Abstract: | It is different from the past reasch of competitive web-site system which only considered the situationin reflexive or competition delays. In this paper, a competitive web-site system with reflexive and competition delays was investigated, where the time-delay was regarded as the bifurcation parameter, by analyzing the characteristics equation, the stability of positive equilibrium was investigated, the existence of Hopf bifurcation was proved, and found the volume of critical time-delay when hopf bifurcation was taken; and then verified the conclusion by using numerical simulation. |
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| Keywords: | competition delay reflexive delay web-site system Hopf bifurcation |
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