Quasi-periodic, Chaotic-torus Bursting Oscillations and SlowPassage Effect in Memristive High-pass Filter Circuit
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摘要: 该文提出了一种忆阻高通滤波电路，它是由有源高通RC滤波器与二极管桥级联LC振荡器的忆阻模拟器并联耦合组成的。该文建立了电路方程与系统模型。基于分岔图、相平面图、庞加莱映射等数值仿真，开展了以反馈增益为可调参数的分岔分析，揭示了忆阻高通滤波电路中存在的准周期、混沌环面、混沌和多周期等簇发振荡行为。进一步地，通过快慢分析法，导出了快子系统的Hopf分岔集，并进而阐述了忆阻高通滤波电路慢通道效应的形成机理。最后，基于Multisim电路仿真验证了数值仿真结果。Abstract: A memristive high-pass filter circuit is presented, which is composed of an active high-pass RC filter parallelly coupling with a memristor emulator of diode-bridge cascaded by LC oscillator. The circuit equations and system model are established. Based on bifurcation diagram, phase plane plot, and Poincaré mapping, bifurcation analysis with the feedback gain as adjustable parameter is performed, from which bursting oscillating behaviors including quasi-period, chaotic-torus, chaos, and multiple period that exist in such a memristive high-pass filter circuit are disclosed. Furthermore, through fast-slow analysis method, Hopf bifurcation set of the fast sub-system is derived, with which the formation mechanism of slow passage effect in the memristive high-pass filter circuit is expounded. Finally, the numerical simulation results are validated based on Multisim circuit simulations.
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