da Silva Josiane C, Gusso A, Dantas W G, Ujevic Sebastian
Departamento de Ciências Exatas-EEIMVR, Universidade Federal Fluminense, Volta Redonda, RJ 27255-125, Brazil.
Chaos. 2024 Jun 1;34(6). doi: 10.1063/5.0190660.
Two-frequency excitation has recently emerged as an efficient method to generate strong chaotification of Duffing and Duffing-like dynamical systems with both single- and double-well potentials. For the systems with a double-well potential, large continuous regions with robust chaos (chaotic attractor insensitive to changes in the system parameters) have been predicted to exist when the method is applied. Motivated by these theoretical results, in this work, we investigate experimentally the chaotification under two-frequency excitation of a simple electronic circuit analogous to the double-well Duffing oscillator. The experimental results confirm the theoretical expectations, and a strong chaotification is observed. Evidences are also presented that the chaotic attractor is robust. Therefore, the work establishes experimentally the two-frequency excitation as a simple and reliable method of chaotification. Furthermore, because of its ease of fabrication, the experimental results turn the particular circuit considered in this work into an interesting practical alternative as a reliable source of continuous-time chaotic signals.
双频激励最近已成为一种有效的方法，可对具有单阱和双阱势的杜芬及类杜芬动力系统产生强烈的混沌化。对于具有双阱势的系统，当应用该方法时，预计会存在具有鲁棒混沌的大连续区域（对系统参数变化不敏感的混沌吸引子）。受这些理论结果的启发，在这项工作中，我们对一个类似于双阱杜芬振荡器的简单电子电路在双频激励下的混沌化进行了实验研究。实验结果证实了理论预期，并观察到了强烈的混沌化。还给出了证据表明混沌吸引子是鲁棒的。因此，这项工作通过实验确立了双频激励是一种简单可靠的混沌化方法。此外，由于其易于制造，实验结果使这项工作中所考虑的特定电路成为一个有趣的实用选择，作为连续时间混沌信号的可靠来源。
