Analysis on the symmetric fast-slow behaviors in a van der Pol-Duffing-Jerk oscillator
Analysis on the symmetric fast-slow behaviors in a van der Pol-Duffing-Jerk oscillator
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DOI：
10.1088/1402-4896/acfce1
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发表时间：
2023-09
期刊：
影响因子：
2.9
通讯作者：
Weipeng Lyu;Shaolong Li;Juanjuan Huang;Qinsheng Bi
中科院分区：
文献类型：
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作者：
Weipeng Lyu;Shaolong Li;Juanjuan Huang;Qinsheng Bi
频域多尺度效应引起的爆破振荡研究是电路系统理论分析中的关键科学问题之一。本文研究了具有慢变参数和外部周期激励的van der Pol-Duffing-Jerk电路振荡器的爆破振荡机理。提出了三种典型爆破模式，即左右对称的“次hopf /褶极限环”爆破、原点对称的“褶/褶极限环”爆破和原点对称的“褶/次hopf /褶极限环”爆破。将缓变激励作为广义状态变量，分析了缓变激励对平衡态和分岔态的临界流形的影响。利用分岔理论，计算出了折叠分岔和Hopf分岔的临界条件，并根据不同分岔曲线的位置，得到了两种典型的分岔结构。在分岔分析的基础上，研究了不同爆破振荡形式随外加激励幅值变化的动态演化规律。指出分叉结构和褶皱与Hopf分叉点之间的距离都会影响破裂模式。我们发现轨迹方向和爆破类型对外激励幅值敏感。此外，我们通过将（θ, x）平面上的轨迹叠加到相应的分岔结构上，揭示了爆破振荡的机理。通过数值模拟验证了理论分析的正确性。
The study of bursting oscillations induced by frequency-domain multiscale effect is one of the key scientific issues in the theoretical analysis of circuit systems. In this paper, we explore the mechanism of the bursting oscillations of a van der Pol-Duffing-Jerk circuit oscillator with slow-changing parametric and external periodic excitations. Three typical bursting modes, namely, left-right symmetric ‘subHopf/fold limit cycle’ bursting, origin symmetric ‘fold/fold limit cycle’ bursting and origin symmetric ‘fold/subHopf/fold limit cycle’ bursting, are presented. The slowly changing excitation is treated as a generalized state variable to analyze the influence on the critical manifolds of the equilibria and bifurcations. The critical conditions of fold and Hopf bifurcations are computed by using the bifurcation theory, and two typical bifurcation structures are obtained according to the position of different bifurcation curves. Based on the bifurcation analysis, we investigate the appearance and dynamicalal evolutions of the different bursting oscillations with the variation of the external excitation amplitude. It is pointed that not only the bifurcation structures but also the distance between the fold and Hopf bifurcation points can affect the bursting patterns. We find the directions of the trajectories and the bursting types are sensitive to the values of the external excitation amplitude. Furthermore, we reveal the mechanism of the bursting oscillations by overlapping the trajectories on (θ, x)-plane onto the corresponding bifurcation structures. Numerical simulations are also presented to prove the correctness of the theoretical analysis in our study.