Departamento de Física, Universidade do Estado de Santa Catarina, 89223-100 Joinville, Brazil.
Chaos. 2011 Sep;21(3):033105. doi: 10.1063/1.3615232.
We report numerical results on the existence of periodic structures embedded in chaotic and hyperchaotic regions on the Lyapunov exponent diagrams of a 4-dimensional Chua system. The model was obtained from the 3-dimensional Chua system by the introduction of a feedback controller. Both the largest and the second largest Lyapunov exponents were considered in our colorful Lyapunov exponent diagrams, and allowed us to characterize periodic structures and regions of chaos and hyperchaos. The shrimp-shaped periodic structures appear to be malformed on some of Lyapunov exponent diagrams, and they present two different bifurcation scenarios to chaos when passing the boundaries of itself, namely via period-doubling and crisis. Hyperchaos-chaos transition can also be observed on the Lyapunov exponent diagrams for the second largest exponent.
我们报告了在 4 维蔡氏系统的李雅普诺夫指数图中，混沌和超混沌区域中嵌入的周期结构的数值结果。该模型是通过引入反馈控制器从 3 维蔡氏系统获得的。在我们丰富多彩的李雅普诺夫指数图中，同时考虑了最大和第二大李雅普诺夫指数，这使我们能够描述周期结构和混沌与超混沌区域。在一些李雅普诺夫指数图中，虾形的周期结构似乎变形了，它们在通过自身边界时呈现出两种不同的通向混沌的分岔情景，即倍周期分岔和突变。在第二大李雅普诺夫指数图中也可以观察到超混沌-混沌转变。
