一种忆感器模型及其振荡器的动力学特性研究

Study on dynamical characteristics of a meminductor model and its meminductor-based oscillator

忆感器是在忆阻器基础上定义的一种新型记忆电路元件.在实际忆感器尚未实现的情况下,为探索忆感器及其在非线性电路中的特性,提出了一种忆感器数学模型和电路模型.基于该模型设计了一个非线性振荡电路,采用理论分析、仿真分析和实验验证的方法研究了忆感器模型的特性及其在电路中的动力学规律.分岔分析表明,在适当的参数下忆感器会使电路产生周期和混沌振荡.设计了实现忆感器模型及其振荡器的模拟电路,实验验证了忆感器模型和振荡器的特性,实验结果与理论分析完全一致.

A meminductor is a new type of nonlinear inductor with memory, which is generalized from the concept of a memristor and defined by current-flux. This paper presents a flux-controlled meminductor model with a smooth quadratic function and designs its corresponding equivalent circuit, which can be used as an emulator to imitate the behavior of a meminductor when actual solid-state meminductor has not yet appeared. Furthermore, a new chaotic oscillator is designed based on this meminductor model, and the dynamical behaviors of the oscillator are investigated, such as chaotic attractors, equilibrium points, Lyapunov exponent spectrum, bifurcations and dynamical map of the system,etc. Bifurcation analysis shows that the meminductor can make the oscillator produce periodic and chaotic oscillations.Moreover, an analog circuit is designed to confirm the correction of the proposed oscillator using the proposed equivalent circuit model of meminductor. It is shown that the experimental results are in good agreement with that of the numerical simulations and the theoretical analysis.