A tri-stable Van der Pol system&rsquo;s stochastic P-bifurcation circuit experiment

PDF(2915 KB)

Journal of Vibration and Shock ›› 2018, Vol. 37 ›› Issue (13) : 111-116.

A tri-stable Van der Pol system’s stochastic P-bifurcation circuit experiment

WU Zhi-qiang WANG Wen-bo ZHANG Xiang-yun

Author information +

History +

Abstract

A Van der Pol circuit system with one stable equilibrium point and two stable limit cycles under the excitation of Gaussian white noise was designed for stochastic dynamics experiment. The effects of Gaussian white noise intensity change on the switching behavior among three steady states of the system was experimentally studied from three aspects including response amplitude time history diagram, phase diagram, and steady state probability density diagram. The results shown that with increase in excitation intensity, the switching frequency among different attractors varies significantly; the relative height between peaks and the peak number of the probability density curve change; Moreover, the distribution of experiment data points in the phase diagram gradually tends to equalization; compared with the theoretical results, the occurrence of the stochastic P-bifurcation phenomenon was qualitatively verified.

Key words

tri-stable Van der Pol circuit / Gaussian white noise / steady-state switching / stochastic P-bifurcation

Cite this article

EndNote

Ris (Procite)

Bibtex

Download Citations

WU Zhi-qiang WANG Wen-bo ZHANG Xiang-yun. A tri-stable Van der Pol system’s stochastic P-bifurcation circuit experiment[J]. Journal of Vibration and Shock, 2018, 37(13): 111-116

References

[1] Javed U, Abdelkefi A, Akhtar I. An improved stability characterization for aeroelastic energy harvesting applications [J]. Communications in Nonlinear Science and Numerical Simulation, 2016, 36: 252-265.
[2] Dimitriadis G, Li J. Bifurcation behavior of airfoil undergoing stall flutter oscillations in low-speed wind tunnel [J]. Aiaa Journal, 2009, 47(47):2577-2596.
[3] Lee B H K, Liu L, Chung K W. Airfoil motion in subsonic flow with strong cubic nonlinear restoring forces [J]. Journal of Sound and Vibration, 2005: 699-717.
[4] Iwnicki S. Handbook of Railway Vehicle Dynamics [M]. CRC/Taylor & Francis, 2006.
[5] Païdoussis M P, Price S J, De Langre E. Fluid-structure interactions: Cross-flow-induced instabilities [M]. Cambridge University Press, 2010.
[6] 顾仁财, 许勇, 郝孟丽, 等. Lévy稳定噪声激励下的duffing-van der pol振子的随机分岔 [J]. 物理学报, 2011, 60(06): 157-161.
GU Ren-cai, XU Yong, HAO Meng-li, et al. Stochastic bifurcations in Duffing-van der Pol oscillator with Lévy stable noise [J]. Acta Physica Sinica, 2011, 60(06): 157-161.
[7] XU Yong, GU Ren-cai, ZHANG Hui-qing, et al. Stochastic bifurcations in a bistable Duffing-van der pol oscillator with colored noise [J]. Phys Rev E Stat Nonlin Soft Matter Phys, 2011, 83(5): 56211-56215.
[8] Zakharova A, Vadivasova T, Anishchenko V, et al. Stochastic bifurcations and coherencelike resonance in a self-sustained bistable noisy oscillator [J]. Physical Review E, 2010, 81(1): 95-102.
[9] 吴志强, 郝颖. 随机激励van der pol-duffing方程三峰p-分岔 [J]. 中国科学:物理学力学天文学, 2013, 43(04): 524-529.
WU Zhi-qiang, HAO Ying. Three-peak P-bifurcations in stochastically excited van der pol- duffing oscillator [J]. Sci Sin-Phys Mech Astron, 2013, 43(04): 524-529.
[10] 郝颖, 吴志强. 三稳态van der pol-duffng振子的随机p分岔 [J]. 力学学报, 2013, 45(02): 257-264.
HAO Ying, WU Zhi-qiang. Stochastic P-bifurcation of tri-stable van der pol--duffing oscillator [J]. Chinese Journal of Theoretical and Applied Mechanics, 2013, 45(02): 257-264.
[11] Zakharova A, Feoktistov A, Vadivasova T, Schöll E. Coherence resonance and stochastic synchronization in a nonlinear circuit near a subcritical Hopf bifurcation [J]. The European Physical Journal Special Topics, 2013, 222(10): 2481-2495.
[12] Semenov V, Feoktistov A, Vadivasova T, et al. Time-delayed feedback control of coherence resonance near subcritical Hopf bifurcation: Theory versus experiment [J]. Chaos, 2014, 25(3):807-813.
[13] 吴志强, 张宝强. 基于9阶van der pol方程的三稳态电路设计及实现 [J]. 天津大学学报(自然科学与工程技术版), 2016(07): 709-715.
WU Zhi-qiang, ZHANG Bao-qiang. Design and implementation of tri-stable circuit based on the ninth-order van der pol equation [J]. Journal of Tianjin University (Science and Technology), 2016(07): 709-715.
[14] 朱位秋. 随机振动(朱位秋) [M]. 北京: 科学出版社, 北京, 1998.
[15] 张肃文. 高频电子线路-第5版 [M]. 高等教育出版社, 北京, 2009.