Oscillatory Circuits With a Real Non-Volatile Stanford Memristor Model

Abstract

Stanford memristor model is a widely used model that accurately characterizes real nonvolatile metal-oxide resistive random access memory (RRAM) devices with bipolar switching characteristics. The paper studies for the first time the dynamics and bifurcations in a class of nonlinear oscillators with real non-volatile memristor devices obeying Stanford model. This is in contrast with papers in the literature considering oscillators with ideal, abstract, or artificial memristor models, that are unable to describe physical memristors implemented in nanotechnology. One main new idea in the paper is to use the memristor as a programmable nonlinear resistor. Namely, two principal modes of operation are considered. 1) Analogue transient phase: the oscillator is designed so that in the transient oscillations the voltage on the memristor is below threshold, hence the main memristor state variable, i.e., the gap of the insulating material, is almost constant and the memristor behaves as a static nonlinear resistor. 2) Programming phase: the nonlinear characteristic of the memristor, which depends on the gap, can be changed via the application of voltages above threshold. The paper studies nonlinear oscillations in the transient phase for a fixed gap as well as the bifurcations phenomena displayed when the gap is varied. The paper also discusses the differences between the approach in the paper and those to design other memristor oscillators with nonvolatile memristors.INDEX TERMS Bifurcations, Chua's circuit, complex dynamics, memristor, Stanford model.

Complete Stability of Neural Networks With Extended Memristors

“…7) CS of a NN, i.e., convergence of each trajectory toward an EP, is a peculiar dynamical property that can be guaranteed under suitable hypotheses on the activations and neuron interconnections (see Assumptions 1 and 2 in Theorem 1). On the other hand, in the general case, NNs do not enjoy CS since they can display sustained oscillations, traveling waves and even chaos and hyperchaos, see, e.g., [29], [59], [60], [61], [62], [63], [64], [65], [66], and references therein.…”

Harmonic Balance Design of Oscillatory Circuits Based on Stanford Memristor Model

“…where T is the temperature, v 0 , q, k, a 0 , ℓ, E ag , E ar , C th , R th , T 0 are given constants (see, e.g., [19]), and γ is a g-dependent local field enhancement factor, given by…”

“…Recently, it has been shown that modeling non-volatile memristors as programmable nonlinear resistors can be fruitfully exploited for the design of oscillatory circuits given by the interconnection of the memristor with a two-terminal linear element [19], [20]. A Chua's oscillatory circuit with a non-volatile extended memristor obeying Stanford model is designed in [19], showing via numerical simulations that it is capable to generate quite different coexisting dynamics. In [20] an oscillatory Chua's circuit based on a non-volatile memristive device is realized and its rich dynamical behavior is validated experimentally.…”

“…In [20] an oscillatory Chua's circuit based on a non-volatile memristive device is realized and its rich dynamical behavior is validated experimentally. In both contributions the design procedure relies on the observation that the memristor state variable (the gap distance in [19]) has almost negligible variations when its voltage is below some threshold. This permits to model the memristor as a nonlinear resistor whose resistance can be programmed for instance by applying voltage pulses above the threshold.…”

“…This paper considers the same circuit of [19], i.e., a nonvolatile extended memristor obeying Stanford model connected to a two-terminal (one port) linear time-invariant element given by the parallel interconnection of the classic Chua's circuit and a linear resistor with negative conductance. The goal is to develop a systematic procedure to design the parameters of the two-terminal element in order to ensure that some given equilibrium point of the circuit undergoes a supercritical Hopf bifurcation at some given value of the gap distance, thus generating a family of (stable) periodic solutions within some range of the gap.…”