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A modified simple chaotic hyperjerk circuit: coexisting bubbles of bifurcation and mixed-mode bursting oscillations
Zeitschrift für Naturforschung A ( IF 1.8 ) Pub Date : 2020-07-28 , DOI: 10.1515/zna-2020-0022
Gervais Dolvis Leutcho 1, 2 , Jacques Kengne 2 , Alexis Ngoumkam Negou 1, 2 , Theophile Fonzin Fozin 3 , Viet-Thanh Pham 4, 5 , Sajad Jafari 6
Affiliation  

Abstract A relatively simple chaotic hyperjerk circuit, which is the modified chaotic hyperjerk system [Dalkiran and Sprott, IJBC 2016] is proposed and investigated in this paper. Only one semiconductor diode modelled the nonlinear function capable of rich and complex dynamical behaviours of the system. We investigate a new kind of behaviours name “bubbles of bifurcation’’ (referred as BsB hereafter) observed here for the first time in the hyperjerk system. An interesting phenomenon of mixed-mode bursting oscillations (MMBOs) is also investigated. The complex dynamics of the novel oscillator (such as MMBOs, BsB, offset boosting and multistability) with respect to its parameters and initial conditions are uncovered using bifurcation diagrams, Lyapunov exponents (LE) and phase portraits. As another interesting property of this circuit, some parameter regions are determined for the existence of coexisting BsB and the coexistence of asymmetric mixed-mode bursting oscillations. Let us emphasized that the complex phenomena observed in this work is very rare in the literature and henceforth merit dissemination. Finally, a physical circuit is constructed to demonstrate some experimental observation of MMBOs.

中文翻译:

改进的简单混沌 hyperjerk 电路:分叉和混合模式爆裂振荡的共存气泡

摘要 本文提出并研究了一种相对简单的混沌 hyperjerk 电路,即改进的混沌 hyperjerk 系统 [Dalkiran and Sprott, IJBC 2016]。只有一个半导体二极管模拟了非线性函数,能够模拟系统丰富而复杂的动态行为。我们研究了一种新的行为,名称为“分叉气泡”(以下称为 BsB),这是在 hyperjerk 系统中首次观察到的。还研究了混合模式突发振荡 (MMBO) 的一个有趣现象。使用分叉图、李雅普诺夫指数 (LE) 和相图揭示了新型振荡器(例如 MMBO、BsB、偏移增强和多稳态)在其参数和初始条件方面的复杂动力学。作为这个电路的另一个有趣的特性,一些参数区域被确定为共存 BsB 的存在和非对称混合模式突发振荡的共存。让我们强调一下,在这项工作中观察到的复杂现象在文献中非常罕见,因此值得传播。最后,构建了一个物理电路来演示对 MMBO 的一些实验观察。
更新日期:2020-07-28
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