忆阻阈值模型及忆阻应用电路特性研究

Memristor is the fourth fundamental circuit element, but its physical device is still commercially unavailable at present. It is an important way to research on the characteristics of memristor application circuits by using memristor models or generalized memristor emulators. In this project, two aspects of research works are performed around the threshold memristor model and the characteristics of memristor application circuits. 1) In order to solve the problems of the existing memristor models, such as boundary effect, terminal state problem and excessive non-linearity, a new threshold memristor model is proposed, which can indeed describe the HP TiO2 memristor. Based on this model, characteristics of its pinched hysteresis loop and fundamental memristive circuits are studied and equivalent hardware circuit based on discrete components is developed. 2) Application circuits based on the proposed threshold memristor model are constructed, upon which corresponding mathematical modeling, numerical simulation and hardware circuit experiments are performed. Complex dynamics of memristor application circuits are investigated, such as bursting oscillation, multi-stability and hidden attractor. Effects of initial states on the impulsive synchronization of memristive chaotic system are investigated. Related research will contribute to developing potential applications of memristor-based circuits, and providing theoretical guidance for engineering applications.

忆阻是第四种基本电路元件，但目前物理器件仍无法达到商用。借助忆阻模型或者广义忆阻模拟器开展忆阻应用电路特性研究是重要研究途径之一。本项目围绕忆阻阈值模型及忆阻应用电路特性，开展两个方面的研究工作：1）针对已有忆阻模型存在的边界效应、末端状态以及过度非线性化等问题，提出一种真实刻画HP TiO2忆阻物理器件的新型忆阻阈值模型，研究忆阻阈值模型的紧磁滞回线特征及其基本忆阻电路特性，研制基于分立元器件实现的硬件等效电路；2）构建基于忆阻阈值模型的应用电路，开展数学建模、数值仿真与硬件电路实验，研究忆阻应用电路的簇发振荡、多稳定性、隐藏吸引子等复杂动力学特性，探讨状态初值对忆阻混沌电路的脉冲同步性能影响。相关研究成果有助于忆阻电路潜在应用的开发，为工程应用提供理论指导。

忆阻器是第四种基本二端电路元件，有着天然的非线性和可塑性，在数据存储、人工神经形态网络、类脑计算等方面存在着广阔的应用前景。本项目着重在阈值忆阻建模与特性分析，忆阻应用电路复杂动力学现象揭示和机理分析和忆阻初值位移调控和忆阻耦合系统同步等方面进行了广泛而深入研究，主要研究成果如下：.(1) 阈值忆阻建模与特性分析. 基于非线性阈值函数，提出了双曲型阈值忆阻模型和周期性阈值忆阻模型等忆阻阈值模型；相应地，进行了忆阻特性分析、忆阻模型的等效电路实现与电路实验验证。.(2) 忆阻应用电路复杂动力学现象揭示与机理分析. 基于已有的忆阻模型或者忆阻模拟器，构建了忆阻低通滤波电路、忆阻带通滤波电路以及二阶非自治忆阻电路等忆阻混沌电路或系统，并进行了相应的动力学建模；通过分岔分析，揭示了忆阻混沌电路或系统所产生的簇发振荡、多稳定性、隐藏吸引子等非线性现象和产生机理，特别地发现了超级慢通道效应；最后完成了数值仿真与电路实验验证。.(3) 忆阻初值位移调控行为与忆阻耦合系统同步. 首先，研究了忆阻初值对吸引子位移和稳定状态的控制行为，最先提出了忆阻初值位移调控的定义，发现了忆阻初值位移调控的特点与忆导函数是相关的，比如周期性，单调性等。其次，讨论了初值对忆阻耦合系统的同步的影响，发现了耦合系统具有依赖于状态初值的平行偏移同步，并利用Lyapunov分析方法，从理论上定量地解释了初值平行偏移同步的影响。

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