调幅力对改进Van der Pol-Duffing振荡器振动共振、混沌和多稳定性的影响

Journal of Nonlinear Sciences and Applications Pub Date : 2023-07-31 DOI:10.22436/jnsa.016.02.04

C. Miwadinou, L. A. Hinvi, C. Ainamon, A. V. Monwanou

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引用次数: 0

摘要

本文讨论了调幅激励对四分子间反应非线性动力学的影响。用卡尔当法详细地计算了自主非线性化学系统的不动点。通过分岔结构、李雅普诺夫指数和相位肖像研究了混沌的路径。分析了控制力对混沌运动的影响，发现了g = 0(未调制情况)、g (cid:54) = 0 (Ω = nω)时的控制效率;N为自然数，Ωω (cid:54) = pq;P和q是简单正整数。基于AM力的频率关系，详细研究了几种吸引子的共振、滞回和共存现象。分析研究的结果得到了数值模拟的验证和补充

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Effect of an amplitude modulated force on vibrational resonance, chaos, and multistability in a modified Van der Pol-Duffing oscillator

This paper deals with the effects of an amplitude modulated (AM) excitation on the nonlinear dynamics of reactions between four molecules. The computation of the ﬁxed points of the autonomous nonlinear chemical system has been made in detail using Cardan’s method. Routes to chaos have been investigated through bifurcations structures, Lyapunov exponent and phase portraits. The effects of the control force on chaotic motions have been strongly analyzed and the control efﬁciency is found in the cases g = 0 (unmodulated case), g (cid:54) = 0 with Ω = nω ; n a natural number and Ωω (cid:54) = pq ; p and q are simple positive integers. Vibrational Resonance (VR), hysteresis and coexistence of several attractors have been studied in details based on the relationship between the frequencies of the AM force. Results of analytical investigations are validated and complemented by numerical simulations

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Journal of Nonlinear Sciences and Applications MATHEMATICS, APPLIED-MATHEMATICS

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期刊介绍： The Journal of Nonlinear Science and Applications (JNSA) (print: ISSN 2008-1898 online: ISSN 2008-1901) is an international journal which provides very fast publication of original research papers in the fields of nonlinear analysis. Journal of Nonlinear Science and Applications is a journal that aims to unite and stimulate mathematical research community. It publishes original research papers and survey articles on all areas of nonlinear analysis and theoretical applied nonlinear analysis. All articles are fully refereed and are judged by their contribution to advancing the state of the science of mathematics. Manuscripts are invited from academicians, research students, and scientists for publication consideration. Papers are accepted for editorial consideration through online submission with the understanding that they have not been published, submitted or accepted for publication elsewhere.