Based on the original stretch-twist-fold flow, we propose a unified stretch–twist–fold (USTF) flow. We explore the conditions that zero-Hopf bifurcation occurs at the origin. Using the first-order averaging theorem, a periodic solution produced from the zero-Hopf equilibrium is derived. In addition, we obtain the conclusion that for parameter \(\alpha \) large enough, the periodic orbit of USTF flow exists as well unstable. Finally, circuit design has been built for implementing the new system, showing a good agreement between computer simulations and experimental observations.

中文翻译：

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统一伸缩流中混沌的周期解与电路设计

基于原始的拉伸-扭曲-折叠流程，我们提出了统一的拉伸-扭曲-折叠（USTF）流程。我们探索在原点发生零 Hopf 分岔的条件。使用一阶平均定理，可以推导出由零-Hopf 平衡产生的周期解。此外，我们得出结论，当参数\(\alpha \)足够大时，USTF流的周期轨道也存在不稳定。最后，为实现新系统建立了电路设计，显示了计算机模拟和实验观察之间的良好一致性。