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具有扩散的广义Brusselator系统的Hopf分歧

郭改慧 吴建华 任小红 于鹏

郭改慧, 吴建华, 任小红, 于鹏. 具有扩散的广义Brusselator系统的Hopf分歧[J]. 应用数学和力学, 2011, 32(9): 1100-1109. doi: 10.3879/j.issn.1000-0887.2011.09.009
引用本文: 郭改慧, 吴建华, 任小红, 于鹏. 具有扩散的广义Brusselator系统的Hopf分歧[J]. 应用数学和力学, 2011, 32(9): 1100-1109. doi: 10.3879/j.issn.1000-0887.2011.09.009
GUO Gai-hui, WU Jian-hua, REN Xiao-hong, YU Peng. Hopf Bifurcation in the General Brusselator System With Diffusion[J]. Applied Mathematics and Mechanics, 2011, 32(9): 1100-1109. doi: 10.3879/j.issn.1000-0887.2011.09.009
Citation: GUO Gai-hui, WU Jian-hua, REN Xiao-hong, YU Peng. Hopf Bifurcation in the General Brusselator System With Diffusion[J]. Applied Mathematics and Mechanics, 2011, 32(9): 1100-1109. doi: 10.3879/j.issn.1000-0887.2011.09.009

具有扩散的广义Brusselator系统的Hopf分歧

doi: 10.3879/j.issn.1000-0887.2011.09.009
基金项目: 国家自然科学基金资助项目(10971124;11001160);陕西省自然科学基础研究计划资助项目(2009JQ1007;2011JQ1015)
详细信息
    作者简介:

    郭改慧(1979- ),女,河南新郑人,讲师,博士(联系人.E-mail:guogaihui@sust.edu.cn).

  • 中图分类号: O175.26

Hopf Bifurcation in the General Brusselator System With Diffusion

  • 摘要: 在齐次Neumann边界条件下,考虑广义Brusselator系统.首先讨论常微分系统Hopf分歧的存在性,得到渐近稳定的周期解.其次讨论具有扩散的偏微分系统,在扩散系数满足一定的条件下,得到超临界的Hopf分歧,并利用规范形理论和中心流形定理给出空间齐次周期解的渐近稳定性.最后,借助Matlab软件进行数值模拟,证明了定理的结论.同时,正平衡态解和空间非齐次周期解的描绘补充了理论分析结果.
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出版历程
  • 收稿日期:  2010-11-04
  • 修回日期:  2011-06-08
  • 刊出日期:  2011-09-15

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