非线性Duffing扰动振子共振机制的研究

数学物理学报 ›› 2018, Vol. 38 ›› Issue (1): 190-196.

非线性Duffing扰动振子共振机制的研究

欧阳成¹, 莫嘉琪²

1. 湖州师范学院理学院浙江湖州 313000;
2. 安徽师范大学数学和计算机科学学院安徽芜湖 241003

收稿日期:2016-03-22 修回日期:2017-07-29 出版日期:2018-02-26 发布日期:2018-02-26
通讯作者: 莫嘉琪 E-mail:mojiaqi@mail.ahnu.edu.cn
作者简介:欧阳成,oyc@hutc.zj.cn
基金资助:
国家自然科学基金（11771005）和浙江省自然科学基金（LY13A010005）

Study of Nonlinear Duffing Disturbed Oscillator for Resonance Mechanism

Ouyang Cheng¹, Mo Jiaqi²

1. Faculty of Science, Huzhou University, Zhejiang Huzhou 313000;
2. School of Mathematics & Computer Science, Anhui Normal University, Anhui Wuhu 241003

Received:2016-03-22 Revised:2017-07-29 Online:2018-02-26 Published:2018-02-26
Supported by:
Supported by the NSFC (11771005) and the Natural Science Foundation of Zhejiang Province (LY13A010005)

摘要/Abstract

摘要： 研究了一类广义Duffing扰动共振机制.利用泛函分析同伦映射方法，构造了求得问题渐近解的迭代关系式.首先求出了Duffing模型的初始近似函数；其次利用迭代关系依次求出了模型的各次渐近解；然后通过举例，说明了用泛函同伦映射方法得到的广义Duffing扰动振子随机共振机制的近似解简单而有效.讨论了得到的渐近解的意义.

关键词: 扰动, 共振, 渐近解

Abstract: A class of nonlinear generalized Duffing disturbed mechanism is considered. The typical Duffing oscillator for resonance mechanism was found. Using the functional mapping method for the problem, a iteration of asymptotic solutions was constructed. Firstly, the initial approximate function of the Duffing model was obtained. Next, applied iteration relation, the arbitrary times asymptotic solutions to the model were solved successively. Then for a example, the generalized Duffing disturbed oscillator for stochastic resonance mechanism by using the functional homotopic mapping method was simple and valid. Finally, the importance foe the obtained asymptotic solutions was illustrated.

Key words: Disturbed, Resonance, Asymptotic solution

中图分类号:

O175.14

欧阳成, 莫嘉琪. 非线性Duffing扰动振子共振机制的研究[J]. 数学物理学报, 2018, 38(1): 190-196.

Ouyang Cheng, Mo Jiaqi. Study of Nonlinear Duffing Disturbed Oscillator for Resonance Mechanism[J]. Acta mathematica scientia,Series A, 2018, 38(1): 190-196.

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