摘要
把弱周期干扰力作用下的含平方项软弹簧Duffing方程作为受小摄动的Hamilton可积系统,给出了对应于由异宿轨道构成的异宿环的Melnikov函数,由此得到系统的浑沌阈。与以往的数值结果进行比较,误差较小,并列举产生误差的原因。
Treating the soft-spring Duffing equation containing a quadratic term under a weak periodic disturbance as a Hamiltonian integrable system under a small perturbation, a Melnikov function is given corresponding to the homoclinic cycle formed by heteroclinic orbits, thus obtaining a chaos threshold of the system. The results calculated numerically show smaller error than previously calculated,and the causes for the error are discussed.
关键词
软弹簧
DUFFING方程
浑沌阈
Duffing equation, chaos threshold, heteroclinic orbit, Melnikov method.
