非线性Duffing扰动振子共振机制的研究

Study of Nonlinear Duffing Disturbed Oscillator for Resonance Mechanism

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.

A class of nonlinear generalized Dulling 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.