| 具有扩散的广义Brusselator系统的Hopf分歧 |
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| 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 |
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| 作者姓名： | 郭改慧 吴建华 任小红 于鹏 |
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| 作者单位： | 陕西科技大学 理学院, 西安 710021; |
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| 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) |
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| 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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| 关 键 词： | 广义Brusselator系统 Hopf分歧 扩散 稳定性 |
| 收稿时间： | 2010-11-04 |
Hopf Bifurcation in the General Brusselator System With Diffusion |
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| 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 |
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| Authors: | GUO Gai-hui WU Jian-hua REN Xiao-hong YU Peng |
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| Affiliation: | College of Science, Shaanxi University of Science and Technology, Xi'an 710021, P. R. China;College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, P. R. China |
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| Abstract: | The general Brusselator system was considered under homogeneous Neumann boundary conditions.The existence results of Hopf bifurcation to the ODE and PDE models were obtained.By the center manifold theory and the normal form method,the bifurcation direction and stability of periodic solutions were also established.Moreover,some numerical simulations were shown to support the analytical results.At the same time,the figures of positive steady-state solutions and spatially inhomogeneous periodic solutions were ... |
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| Keywords: | general Brusselator system Hopf bifurcation diffusion stability |
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