Nonlinear dynamic approach to the analysis of memristor parameters instability

A general set of ideas related to the memristors modeling is presented. The memristor is considered to be a partially ordered physical and chemical system that is within the “edge of chaos“ from the point of view of nonlinear dynamics. The logical and historical relationship of memristor physics, nonlinear dynamics, and neuromorphic systems is illustrated in the form of a scheme. We distinguish the nonlinearity into external ones, when we describe the behavior of an electrical circuit containing a memristor, and internal ones, which are caused by processes in filament region. As a simulation model, the attention is drawn to the connectionist approach, known in the theory of neural networks, but applicable to describe the evolution of the 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 meaning of the theory of coupled maps lattice is indicated. The high-density current through the filament can lead to the need to take into account both discrete processes (generation of traps) and continuous processes (inclusion of some constructions of solid body theory into the model).
However, a compact model is further developed in which the state of such a network is aggregated to three phase variables: the length of the filament, its total charge, and the local temperature. Despite the apparent physical meaning, all variables have a formal character, which is usually inherent in the parameters of compact models. The model consists of one algebraic equation, two differential equations, and one integral connection equation, and is derived from the simplest Strukov’s model. Therefore, it uses the “window function” approach. It is indicated that, according to the Poincare—Bendixon theorem, this is sufficient to explain the instability of four key parameters (switching voltages and resistances ON/OFF) at a cycling of memristor. The Fourier spectra of the time series of these parameters are analyzed on a low sample of experimental data. The data are associated with the TiN/HfOx/Pt structure (0 < x < 2). A preliminary conclusion that requires further verification is the predominance of low frequencies and the stochasticity of occurrence ones.

memristor, nonlinear dynamics, connectionism, compact model, cycling

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