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首页> 外文期刊>Analog Integrated Circuits and Signal Processing >Dynamics, control and symmetry breaking aspects of a modified van der Pol-Duffing oscillator, and its analog circuit implementation
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Dynamics, control and symmetry breaking aspects of a modified van der Pol-Duffing oscillator, and its analog circuit implementation

机译：改进van der Pol-Duffing振荡器的动态，控制和对称性破坏方面及其模拟电路实现

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摘要

This article focuses on the dynamics of a modified van der Pol-Duffing circuit (MVDPD hereafter) (Fotsin and Woafo in Chaos Solitons and Fractals 24(5):1363-1371, 2005) whose symmetry is explicitly broken with the presence an offset term. When ignoring offset terms, the system displays an exact symmetry which is reflected in the location of the equilibrium points, the attractor topologies and the attraction basins shapes as well. In this mode of operation, the system displays typical behaviors such as period doubling sequences; spontaneous symmetry breaking, symmetry recovering, and multistability involving several pairs of mutually symmetric attractors. In the presence of offset terms, the MVDPD circuit is non-symmetric and more complex nonlinear phenomena arise such as parallel bifurcation branches, coexisting multiple (i.e. two, three, four or five) asymmetric attractors, and crises. It should be noted that for each case of multistability discussed in this work, a hidden attractor (period-1 limit cycle) coexists with self-excited others. To the best of our knowledge, the coexistence of five attractors (symmetrical or asymmetrical), one of which is hidden has not yet been reported in the MVDPD circuit and thus deserves dissemination. PSpice simulation investigations based on the implementation of the MVDPD confirm the theoretical predictions.
机译：本文重点介绍了改进的范德波Duffing电路（以下MVDPD）的动态（在混沌孤子和分数龙中的FOTSIN和WOAFO 24（5）：1363-1371,2005），其对称性被存在偏移项明确地破坏。当忽略偏移术语时，系统显示精确的对称性，其反映在均衡点，吸引子拓扑和吸引盆地形状的位置。在这种操作模式中，系统显示典型的行为，例如倍增倍率序列;自发对称性断裂，对称恢复和涉及几对相互对称的吸引子的多重性。在偏移术语的存在中，MVDPD电路是非对称的，并且产生的非对称和更复杂的非线性现象，例如并联分支分支，共存多个（即二，三，四或五个）不对称的吸引子和危机。应该注意的是，对于在这项工作中讨论的每种类型的多个案例，隐藏的吸引子（周期-1限制周期）与自我激动的其他人共存。据我们所知，五个吸引子（对称或不对称）的共存，其中一个被隐藏在MVDPD电路中尚未报告，因此值得传播。基于MVDPD实施的PSPICE仿真调查证实了理论预测。

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