Generating chaos via x|x|
Generating chaos via x|x|
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DOI：
10.1109/81.922468
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发表时间：
2001-05
影响因子：
5.1
通讯作者：
K. Tang;K. Man;G. Zhong;Guanrong Chen
中科院分区：
文献类型：
--
作者：
K. Tang;K. Man;G. Zhong;Guanrong Chen
本文研究了函数 x|x| 的作用作为非自治系统中的混沌发生器。使用类达芬非自治振荡器进行说明。通过 Melnikov 函数方法严格证明，这种特殊的二次函数将 Smale 马蹄形引入类 Duffing 系统。此外，还论证了其作为能量函数的物理意义，为混沌的出现提供了临界值。为了更好地理解潜在的动力学，给出了分叉分析的模拟。
This paper investigates the role of the function x|x| as a chaos generator in nonautonomous systems. A Duffing-like nonautonomous oscillator is used for illustration. It is rigorously proven via the Melnikov function method that this particular quadratic function induces Smale horseshoes to the Duffing-like system. Moreover, its physical meaning as an energy function is demonstrated, which provides a critical value for the emergence of chaos. Simulations with bifurcation analysis are given for better understanding of the underlying dynamics.