【摘要】 建立某纳米尺度振荡器的非线性振动模型,利用李雅谱诺夫特征指数判别该系统是否发生混沌运动。针对系统发生混沌运动时,利用标准的显式龙格—库塔积分法计算李雅谱诺夫特征指数的数值不稳定性问题,提出利用隐式的龙格—库塔辛积分法进行数值积分,并对李雅谱诺夫向量进行修正,获得收敛的李雅谱诺夫特征指数。更多还原

【Abstract】 A model of nonlinear vibration for a nano-oscillator was developed.Lyapunov characteristic exponents(LCEs) provide quantitative criteria allowing one to distinguish between regular and chaotic behaviors for the dynamical system.It is difficult to perform numerical integration in terms of standard explicit Runge-Kutta method to obtain the converged LCEs when the motion of system is chaotic.The implicit and symplectic Runge-Kutta approach was presented to solve the differential equations in which the norm of Lyapunov direction vector is corrected to avoid the emergence of overflow error,and the converged LCEs can be solved by means of this algorithm.更多还原