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 Nonlin Soft Matter Phys. 2003 Dec;68(6 Pt 2):066217. doi: 10.1103/PhysRevE.68.066217. Epub 2003 Dec 31.
Well-behaved dynamical properties are found in a dissipative kicked rotator subjected to a periodic string of asymmetric pulses of finite amplitude and width. The stability boundaries of the equilibrium are determined to arbitrary approximation for trigonometric pulses by means of circular harmonic balance, and to first approximation for general elliptic pulses by means of an elliptic harmonic balance method. The bifurcation behavior at the stability boundaries is determined numerically. We show how the extension of the instability region of the equilibrium in pulse parameter space reaches a maximum as the pulse width is varied. We also characterize the dependence of the mean duration of the transients to the equilibrium on the pulse width. The evolution of the basins of attraction of chaotic attractors when solely the pulse width is varied is characterized numerically. Finally, we show that the order-chaos route when solely the width of the pulses is altered appears to be especially rich, including different types of crises. The mechanism underlying these reshaping-induced crises is discussed with the aid of a two-dimensional map.
在一个耗散型受驱转子中发现了良好的动力学特性，该转子受到一串具有有限幅度和宽度的非对称脉冲的周期性作用。通过圆谐平衡法可任意近似地确定三角脉冲作用下平衡态的稳定性边界，通过椭圆谐平衡法可一阶近似地确定一般椭圆脉冲作用下平衡态的稳定性边界。在稳定性边界处的分岔行为通过数值方法确定。我们展示了随着脉冲宽度的变化，平衡态不稳定区域在脉冲参数空间中的扩展如何达到最大值。我们还刻画了暂态到平衡态的平均持续时间对脉冲宽度的依赖性。通过数值方法刻画了仅改变脉冲宽度时混沌吸引子吸引域的演化。最后，我们表明仅改变脉冲宽度时的有序 - 混沌路径似乎特别丰富，包括不同类型的危机。借助二维映射讨论了这些由重塑引发的危机背后的机制。
