Chacón R, Martínez García-Hoz A
Departamento de Electrónica e Ingeniería Electromecánica, Escuela de Ingenierías Industriales, Universidad de Extremadura, Apartado Postal 382, E-06071 Badajoz, Spain.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1999 Jun;59(6):6558-68. doi: 10.1103/physreve.59.6558.
We study a parametrically damped two-well Duffing oscillator, subjected to a periodic string of symmetric pulses. The order-chaos threshold when altering solely the width of the pulses is investigated theoretically through Melnikov analysis. We show analytically and numerically that most of the results appear independent of the particular wave form of the pulses provided that the transmitted impulse is the same. By using this property, the stability boundaries of the stationary solutions are determined to first approximation by means of an elliptic harmonic balance method. Finally, the bifurcation behavior at the stability boundaries is determined numerically.
我们研究了一个参数阻尼双阱杜芬振子，它受到一串周期性的对称脉冲作用。通过梅尔尼科夫分析从理论上研究了仅改变脉冲宽度时的有序 - 混沌阈值。我们通过解析和数值方法表明，只要传输的冲量相同，大多数结果似乎与脉冲的具体波形无关。利用这一特性，借助椭圆谐波平衡法将定态解的稳定性边界确定到一阶近似。最后，通过数值方法确定稳定性边界处的分岔行为。
