Abstract
A number of important applications would benefit from the introduction of locally-active memristors, which is defined to be any memristor that exhibits negative differential memristance for at least a voltage or a current applied to the memristor. Two leading examples are emerging nonvolatile memory based on memristor-based crossbar array architectures, and neural networks that exhibit improved computational complexity when operated at the edge of chaos. In this paper, a novel locally-active memristor model is presented for exploring the nonvolatile and switching mechanism of the memristor and the influence of local activity on the complexity of nonlinear circuits. We find that the memristor possesses three locally-active regions in its DC [Formula: see text]–[Formula: see text] plot and two asymptotically stable states (equilibrium points) on its power-off plot (POP) where voltage [Formula: see text], implying that the memristor is bistable, which can be used as a nonvolatile binary memory or binary switch. We also find the mechanism and the rule of switching between the two stable states by applying a single square voltage pulse of appropriate pulse width and pulse amplitude. We show that it is always possible to switch from one stable state to another of the memristor with an appropriate pulse amplitude and a pulse width, and that there is a trade-off between the voltage pulse amplitude and the pulse width for the faster switching between the two equilibrium points. We also show that fast switching between the two states is possible by using a periodic bipolar narrow pulse sequence. Local activity depends on the capability of a memristor circuit to amplify infinitesimal fluctuations in energy. Based on this principle, we designed a simplest chaotic oscillator that utilizes only three components in parallel: the proposed locally-active memristor, a linear capacitor and an inductor, which can oscillate around an equilibrium point located on its DC [Formula: see text]–[Formula: see text] plot. Its dynamic characteristics are verified by theoretical analyses, simulations and DSP experiments.
Highlights
Memristor is a 2-terminal circuit element that was originally postulated by Chua as the fourth basic circuit element [Chua, 1971]
The dynamics must move to the left, until it returns to the initial point Q0, thereby implying that the switching fails. It follows that for a successful switching from equilibrium point Q0 to Q2, the applied voltage pulse amplitude U must be at least large enough for the minima of the corresponding dynamic route to stay above the x-axis, and that the pulse width W must be at least long enough for the motion of state x(t) to pass beyond the unstable equilibrium state Q1, i.e. the downward jump from the corresponding dynamic route to the power-off plot (POP) must land to the right of the unstable equilibrium Q1, so that it can fall into the attractive region of the equilibrium point Q2
If we switch the memristor from initial state Q0 to Q2, faster switching is possible by using a periodic bipolar narrow pulse sequence and increasing the pulse amplitude U, as shown in Fig. 12, where the retune downward jump just falls on the equilibrium point Q2 on the POP where voltage pulse U = 0
Summary
Memristor is a 2-terminal circuit element that was originally postulated by Chua as the fourth basic circuit element [Chua, 1971]. Kumar et al [2017] reported a nanoscale NbO2 Mott memristor that can be incorporated into a relaxation oscillator, and a tunable range of periodic and chaotic oscillations is implemented. Such locallyactive memristors can be useful in certain types of neural computing by introducing a chaotic pseudorandom signal that can prevent global synchronization and assist in finding a global minimum in a constrained search. The locally-active NbO2 Mott memristor has been used in the Hopfield network for generating oscillation and finding a global minimum during a constrained search [Kumar et al, 2017]. We design a chaotic oscillator using the locallyactive memristor connected in parallel with a linear capacitor and an inductor, and its dynamics are analyzed by theoretical analyses, simulations and DSP experiments
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