Abstract

A general set of ideas related to the modeling of memristors is presented. The memristor is considered as a partially ordered physicochemical system, located in terms of nonlinear dynamics within the “edge of chaos.” The logical-historical relationship of the physics of memristors, nonlinear dynamics, and neuromorphic systems is illustrated in the form of a diagram. Nonlinearity is divided by us into external nonlinearity, when the behavior of an electric circuit containing a memristor is described, and internal nonlinearity, due to processes in the filament volume. In the simulation modeling, attention is drawn to the connectionist approach, well known in the theory of neural networks, but applicable to describe the evolution of a filament as the dynamics of a network of traps connected electrically and quantum mechanically. The state of each trap is discrete and it is called an oscillator. The applied value of the theory of lattices of coupled oscillators is indicated. The flow of high-density current through the filament can lead to the necessity of taking into account both discrete processes (trap generation) and continuous processes (introducing elements of the solid-state band theory into the model). Nevertheless, a compact model is further developed in which the state of such a network is aggregated up to three phase variables: filament length, its total charge, and the local temperature. Despite the apparent physical meaning, all variables have a formal character, usually inherent in the parameters of compact models. The model consists of one algebraic equation, two differential equations, and one integral constraint equation, and it is inherited from the simplest Strukov model. Therefore, it uses the window function approach. It is indicated that, according to the Poincaré–Bendixson theorem, this is sufficient to explain the instability of the four key parameters (switching voltages and resistances) during memristor cycling. The Fourier spectra of the time series of these parameters are analyzed on a small sample of experimental data. The data refer to the structure of TiN/HfO_x/Pt (0 < x < 2). The preliminary conclusion on the predominance of low frequencies and the stochastic appearance of frequencies requires further verification.

中文翻译：

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忆阻器参数不稳定性分析的非线性动力学方法

摘要

提出了与忆阻器建模相关的一般思路。忆阻器被认为是部分有序的物理化学系统，位于“混沌边缘”内的非线性动力学方面。忆阻器物理学，非线性动力学和神经形态系统的逻辑历史关系以图表形式说明。当我们描述包含忆阻器的电路的行为时，我们将非线性分为外部非线性和由于灯丝体积过程引起的内部非线性。在模拟建模中，注意力集中在神经网络理论中众所周知的连接主义方法上，但可用于描述灯丝的演化，将其描述为电和量子机械连接的陷阱网络的动力学。每个陷阱的状态都是离散的，称为振荡器。指出了耦合振荡器晶格理论的应用价值。流过灯丝的高密度电流可能导致需要考虑离散过程（陷阱产生）和连续过程（将固态能带理论的元素引入模型）。尽管如此，仍进一步开发了一个紧凑模型，其中将这种网络的状态汇总到三个相位变量：灯丝长度，其总电荷和局部温度。尽管具有明显的物理含义，所有变量都具有形式特征，通常是紧凑模型的参数固有的。该模型由一个代数方程，两个微分方程和一个积分约束方程组成，它是从最简单的Strukov模型继承而来的。因此，它使用窗口函数方法。结果表明，根据庞加莱－本迪克森定理，这足以说明忆阻器循环期间四个关键参数（开关电压和电阻）的不稳定性。这些参数的时间序列的傅立叶光谱是在少量实验数据样本上进行分析的。数据是指TiN / HfO的结构_x / Pt（0 < x <2）。关于低频的优势和频率的随机出现的初步结论需要进一步验证。