| 一类二维动力系统的稳定性及分叉分析 |
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| 引用本文： | 胡军浩,晏 磊.一类二维动力系统的稳定性及分叉分析[J].中南民族大学学报(自然科学版),2014(4):105-109. |
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| 作者姓名： | 胡军浩 晏 磊 |
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| 作者单位： | 中南民族大学 数学与统计学学院，武汉430074 |
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| 基金项目： | 国家自然科学基金资助项目(61374085) |
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| 摘 要： | 考虑一类由二阶二次差分方程简化而成的二维动力系统,运用Jury条件和稳定性理论研究其动力学行为,分析该系统两个不动点的局部稳定性及其分叉现象,利用数值模拟验证了结果的正确性.最后,应用中心流形定理确定系统不动点在发生Flip分叉时的临界稳定性.
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| 关 键 词： | 动力系统 稳定性 Jury条件 分叉 中心流形定理 |
Stability and Bifurcation Analysis of a Class of Two-Dimensional Dynamical Systems |
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| Hu Junhao;Yan Lei.Stability and Bifurcation Analysis of a Class of Two-Dimensional Dynamical Systems[J].Journal of South-Central Univ for,2014(4):105-109. |
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| Authors: | Hu Junhao;Yan Lei |
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| Institution: | Hu Junhao;Yan Lei;College of Mathematics and Statistics,South-Central University for Nationalities; |
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| Abstract: | In this paper, we consider a class of two-dimensional dynamical system which is simplified from the second order quadratic differential equation, use the Jury condition and stability theory to study the dynamical behavior, analyze the local stability of the two different fixed points and their bifurcation phenomenon, and then we have verified the results by numerical simulations.Finally, we research the critical stability of the fixed points at flip bifurcation with center manifold theorem. |
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| Keywords: | dynamical systems stability Jury condition bifurcation center manifold theorem |
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