摘要
在经典力学框架内和小振幅近似下,把超晶格量子阱的粒子运动方程化为了具有阻尼项、受迫项的广义Duffing方程,并用Jacobian椭圆函数和第一类椭圆积分解析地给出了无扰动系统的解和粒子运动周期;用Melnikov方法构造了异宿轨道的Melnikov函数,并利用Poincare映射分析了异宿轨道在Smale马蹄意义下的混沌行为。结果表明,系统进入混沌的临界条件与它的参数有关,只需适当调节系统参数就可以避免或控制混沌发生,从而保证系统的稳定性。
In the frame of classical mechanics and in the small amplitude approximation,the motion equation of particles in the superlattice quantum well is reduced to the general Duffing equation with a damping term and a forced term,the solution of the equation and the period of the particle motion are expressed exactly by means of Jacobian elliptic function and 1-st kind elliptic integral for the non-perturbed system. The Melnikov function for the heteroclinic orbit is constituted by Melnikov method,and the chaotic behaviours of the heteroclinic orbit in a sense of Smale horseshol are analysed by using Poincare mapping. The results show that the critical condition entering in the chaos is related to the system papameters,then by suitable regulating the parameters of the system,the chaos can be avoided or controlled,then the stability of the system can be ensured.
出处
《半导体光电》
CAS
CSCD
北大核心
2010年第3期422-425,共4页
Semiconductor Optoelectronics
基金
广东省自然科学基金项目(9151065005000008)
