三阶张弛振子的临界行为

Critical Behavior of Cubic Relaxation Oscillator

本文报道最简单三阶张弛振子的实验电路、映象描述,及对其从准周期向混沌过渡的临界行为的实验研究,并说明了这些临界行为的普遍意义。我们测得沿临界线准周期集的分数维为:D=0.88±0.01;以及当绕数逼近黄金分割比时,映象参数的收敛比平均值为:■-2.85±0.1。这些结果与圆映象理论很好地符合,从而对Cumming等人得出的D=0.795±0.005及δ_n 的值在-3.3±0.1与-2.7±0.2之间的结论作了较圆满的解释。

The experimental Circuit,map description,and the experimental study on the critical behavior at the transition from quasiperiodicity to chaos for the symplest cubic relaxation oscillator are reported.The universality of these critical behaviors is explained.The fractal dimension of the quasiperiodic set álong the critical line is measured as D=0.88+0.01;and the of the number convergence ratio of the map parameter when the winding number con- verges goldenmean is(?)=-2.85+0.1.The results are in verry good agreement ith the theory of circle map.That give a good explanation to the results of D=0.795+0.005 and-3.3+0.1 <δ(?)-2.7+0.2 obtained by Cumming et al.