摘要
在经典力学框架内,把偶极子的运动方程化为带有阻尼项和受迫项的广义外尔斯特拉斯方程。在无扰动情况下,用外尔斯特拉斯函数分析了系统的相平面特征;在扰动情况下,用多尺度法讨论了系统的稳定性。结果表明,在相平面上,分支轨道是一条过不稳定点的同宿轨道,系统除了存在ω=ω0的主共振和ω=2ω0的倍频共振外,还存在ω=ω0/2的分频共振。对系统的稳定性分析表明,只需适当选择参数就可以保证系统是稳定的。
In the classical mechanics frame,the motion equation of the dipole is reduced to the general Weierstrass equation with a damping term and a foced term.In the non-perturbed case the phase plane properties are analysed by using Weierstrass function,while in the perturbed case the stabilities of the second-order nonlinear optical system are discussed in terms of the multi-scalar techniques.The results show that the separatrix orbit is a homoclinic orbit through the instable point in the phase plane,there are fraction frequency resonance except for the main resonance of and double frequency resonance of.The analysis of the stability shows that suitable regulations of the parameters can ensure the stability of the system.
出处
《半导体光电》
CAS
CSCD
北大核心
2010年第6期891-894,共4页
Semiconductor Optoelectronics
基金
广东省自然科学基金项目(8151170003000010)
关键词
非线性
稳定性
多尺度法
外尔斯特拉斯函数
nonlinearity
stability
multi-scalar techniques
Weierstrass function
