A new three-dimensional continuous autonomous system is proposed in this paper and it exhibits single scroll chaotic behavior in a particular parameter region. By linear stability analysis and numerical simulations, we investigate different dynamical observations with respect to system parameters and try to understand the route to generation of chaos. For a large portion of the parameter region, we see a sudden birth of a period-three limit cycle. Then the period-three orbit turns into a chaotic state through typical Pomeau-Manneville intermittent route to chaos. Lyapunov exponent and Kaplan-Yorke dimension are used to verify the chaotic behavior. It becomes periodic via inverse period-doubling route for higher values of the parameters. A two-parameter bifurcation diagram is shown which distinguishes the chaotic region from other periodic and steady-state regions.

中文翻译：

---

新混沌系统的行为研究

本文提出了一种新的三维连续自治系统，该系统在特定参数区域内表现出单涡旋混沌行为。通过线性稳定性分析和数值模拟，我们研究了关于系统参数的不同动力学观察结果，并试图了解产生混沌的途径。对于大部分参数区域，我们看到了三个周期的极限周期的突然产生。然后，三个周期的轨道通过典型的Pomeau-Manneville间歇性路径变成混沌，变成混沌状态。使用李雅普诺夫指数和Kaplan-Yorke维数来验证混沌行为。对于更高的参数值，它通过反向周期倍增路径变为周期性。