【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。更多还原

【Abstract】 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.更多还原