Some years ago, Fotsin and Woafo (Phys Scrip 71:241, 2005) introduced and investigated an electronic circuit consisting of Van der Pol oscillator coupled to a linear oscillator, which appeared to be chaotic. Later, some few authors investigated chaos synchronization of this model. However, detail dynamical analyses and experimental verification of this interesting model were not carried out till now. This work thus provides a deeper dynamical analysis and experimental confirmation of the chaotic behavior in this oscillator. Some basic dynamic properties of the system are studied, namely symmetry, dissipation, fixed points with their stability and Hopf bifurcation. It is found that the system displays complicated behaviors such as intermittency, crisis route to chaos, antimonotonicity, bursting oscillations and coexisting attractors for specific values of parameters setting. The coexistence of attractors is illustrated using the phase portraits and cross section of the basin of attraction. Hardware experiments and Pspice-based circuit simulations are included in order to support numerical simulations. To our knowledge, such phenomena have not yet been reported in this oscillator and therefore constitute a significant contribution in understanding of the dynamical behavior of this type of oscillators and their potential applications.

中文翻译：

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VDPCL振荡器的动力学研究：反单调性，爆发振荡，吸引子并存和硬件实验

几年前，Fotsin和Woafo（Phys Scrip 71：241，2005）引入并研究了一种由Van der Pol振荡器与线性振荡器耦合的电子电路，该线性振荡器看上去很混乱。后来，一些作者研究了该模型的混沌同步。但是，到目前为止，尚未对该模型进行详细的动力学分析和实验验证。因此，这项工作为该振荡器中的混沌行为提供了更深入的动力学分析和实验确认。研究了系统的一些基本动力学特性，即对称性，耗散性，具有稳定性的不动点和Hopf分支。发现该系统显示出复杂的行为，例如间歇性，陷入混乱的危机路径，反单调性，对于参数设置的特定值，爆发振荡和吸引子共存。吸引器的共存通过吸引池的相图和横截面进行说明。包括硬件实验和基于Pspice的电路仿真，以支持数值仿真。据我们所知，这种现象尚未在该振荡器中得到报道，因此对理解这种类型的振荡器的动态行为及其潜在应用作出了重大贡献。