| Bifurcations of Invariant Tori and Subharmonic Solutions of Singularly Perturbed System |
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| 作者姓名： | Zhiyong YE Maoan HAN |
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| 作者单位： | Zhiyong YE Maoan HAN Department of Mathematics，Xi'an Jiaotong University，Xi'an 710049，China; Department of Mathematics，Chongqing Institute of Technology，Chongqing 400050，China. Department of Mathematics，Shanghai Normal University，Shanghai 200243，China. |
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| 基金项目： | 国家自然科学基金;重庆市自然科学基金 |
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| 摘 要： | This paper deals with bifurcations of subharmonic solutions and invariant tori generated from limit cycles in the fast dynamics for a nonautonomous singularly perturbed system. Based on Poincare map, a series of blow-up transformations and the theory of integral manifold, the conditions for the existence of invariant tori are obtained, and the saddle-node bifurcations of subharmonic solutions are studied.
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| 关 键 词： | 奇异摄动系统 下调和解 不变圆环面 分歧 |
| 收稿时间： | 25 January 2006 |
Bifurcations of Invariant Tori and Subharmonic Solutions of Singularly Perturbed System |
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| Zhiyong YE,Maoan HAN.Bifurcations of Invariant Tori and Subharmonic Solutions of Singularly Perturbed System[J].Chinese Annals of Mathematics,Series B,2007,28(2):135-148. |
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| Authors: | Zhiyong YE and Maoan HAN |
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| Institution: | 1. Department of Mathematics, Xi'an Jiaotong University, Xi'an 710049, China;Department of Mathematics,Chongqing Institute of Technology, Chongqing 400050, China
2. Department of Mathematics,Shanghai Normal University,Shanghai 200243,China |
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| Abstract: | This paper deals with bifurcations of subharmonic solutions and invariant tori generated from limit cycles in the fast dynamics for a nonautonomous singularly perturbed system. Based on Poincare map, a series of blow-up transformations and the theory of integral manifold, the conditions for the existence of invariant tori are obtained, and the saddle-node bifurcations of subharmonic solutions are studied. |
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| Keywords: | Singular perturbation Subharmonic solution Saddle-Node Invariant torus |
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