超晶格量子阱二阶非线性系统的动力学稳定性

在经典力学框架内和小振幅近似下,引入正弦平方势,把粒子的运动方程化为广义Duffing方程。在二次非线性情况下,把Duffing方程化为外尔斯特拉斯方程,并用外尔斯特拉斯函数分析了系统的相平面特征。用李雅普诺夫方法讨论了系统二次超谐共振,以及系统的稳定与临界条件。结果表明,适当调整参数就可以保证系统状态是稳定的。

Dynamical Stability of the Second-order Nonlinear System for Superlattice Quantum Well

In the framework of classical mechanics and the small amplitude approximation,the particle motion equation is reduced to generalized Duffing equation by introducing sine-squared potential.In the second-order nonlinearity case,the Duffing equation is furtherly reduced to the Weierstrass equation,and the phase plane characteristics of the system are analyzed by using Weierstrass function.The second-order superharmonic resonance,the stability and the critical conditions are discussed by Lyapunov method.The results show that appropriate adjustment on the parameters can guarantee the stability of the system.