Kruglov V P, Krylosova D A, Sataev I R, Seleznev E P, Stankevich N V
Kotelnikov Institute of Radioengineering and Electronics of RAS, Saratov Branch, Zelenaya str. 38, Saratov 410019, Russia.
Chernyshevsky Saratov State University, Astrakhanskaya str. 83, Saratov 410012, Russia.
Chaos. 2021 Jul;31(7):073118. doi: 10.1063/5.0055579.
Transition to chaos via the destruction of a two-dimensional torus is studied numerically using an example of the Hénon map and the Toda oscillator under quasiperiodic forcing and also experimentally using an example of a quasi-periodically excited RL-diode circuit. A feature of chaotic dynamics in these systems is the fact that the chaotic attractor in them has an additional zero Lyapunov exponent, which strictly follows from the structure of mathematical models. In the process of research, the influence of feedback is studied, in which the frequency of one of the harmonics of external forcing becomes dependent on a dynamic variable. Charts of dynamic regimes were constructed, examples of typical oscillation modes were given, and the spectrum of Lyapunov exponents was analyzed. Numerical simulations confirm that chaos resulting from the cascade of torus doubling has a close to the zero Lyapunov exponent, beside the trivial zero exponent.
通过二维环面的破坏向混沌的转变，使用准周期强迫下的亨农映射和托达振荡器的例子进行了数值研究，并且使用准周期激励的RL - 二极管电路的例子进行了实验研究。这些系统中混沌动力学的一个特征是，它们中的混沌吸引子具有额外的零李雅普诺夫指数，这严格源于数学模型的结构。在研究过程中，研究了反馈的影响，其中外部强迫的一个谐波的频率变得依赖于一个动态变量。构建了动态区域图，给出了典型振荡模式的例子，并分析了李雅普诺夫指数谱。数值模拟证实，除了平凡的零指数外，由环面翻倍级联产生的混沌具有接近零的李雅普诺夫指数。
