Asymptotic Solution to a Class of Nonlinear Singular Perturbation Autonomous Differential Systems

FENG Yihu; CHEN Huaijun; MO Jiaqi

doi:10.21656/1000-0887.380110

Volume 39 Issue 3

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FENG Yihu, CHEN Huaijun, MO Jiaqi. Asymptotic Solution to a Class of Nonlinear Singular Perturbation Autonomous Differential Systems[J]. Applied Mathematics and Mechanics, 2018, 39(3): 355-363. doi: 10.21656/1000-0887.380110

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Asymptotic Solution to a Class of Nonlinear Singular Perturbation Autonomous Differential Systems

doi: 10.21656/1000-0887.380110

¹Department of Electronics and Information Engineering, Bozhou College, Bozhou, Anhui 236800, P.R.China;²School of Mathematics & Computer Science, Anhui Normal University, Wuhu, Anhui 241003, P.R.China

Funds: The National Natural Science Foundation of China(11202106)

Received Date: 2017-04-25
Rev Recd Date: 2017-06-07
Publish Date: 2018-03-15

Abstract

Abstract

A class of generalized Lienard singular perturbation systems were considered. Firstly, the reduced solution to the system was obtained. Next, the outer solution was constructed by means of the singular perturbation method. Then, a stretch variable was introduced and the initial layer corrective term was found. Finally, the arbitrary-order asymptotic analytic expansion of the system solution was given and the uniform validity of the solution was proved. The proposed method with the basic theory has wide application values.
- stretch variable,
- singular perturbation,
- autonomous system

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References(27)

References

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