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Is it a fourth fundamental circuit element?

Williams says this is a judgement call. His memristor history docent discusses the notion and includes this diagram:

Memristor

Current-voltage characteristics for the resistor, capacitor, inductor and memristor.

Williams says: "The upper panel shows an applied voltage sine wave (gray) versus time with the corresponding current for a resistor (blue), capacitor (red), inductor (green) and memristor (purple). The lower figures show the current-voltage characteristics for the four devices, with the characteristic pinched hysteresis loop of the memristor in the bottom right. It is nearly obvious by inspection that the memristor curve cannot be constructed by combining the others."

Mouttet's Neuron connection

Chua's memristor ideas developed, Mouttet claims, into a more generalised theoretical framework in 1976, in the form of memristive systems. These were shown to be applicable to the modeling of biological neurons.

An article by Mouttet says: "The recent interest in the memristor theory of Chua was sparked by an article in the journal Nature published by researchers at HP Labs in 2008 reporting memristive effects in TiO2. (Titanium Dioxide)," called "The missing memristor found."

Memristor modelling problems

According to Mouttet, the HP researchers tried to show that memristor theory could be used to model resistive switching effects that occur in several thin-film materials:

A memristive systems model may be mathematically formulated as:

v = R(x) i and dx/dt = m(i)

where x= state variable, v = voltage, i = current, R(x)=memristance function, m(i) = rate of change of the state variable.

Mouttet says the models developed by HP have problems, such as not taking memcapacitive effects into account, being poorly formulated for electrical engineering applications, not distinguishing between internal and external electric fields. He claims HP's newer models do not actually represent memristors at all5.

... the models used by HP in describing Pt-TiO-Pt have diverged from the original Nature paper and no longer describe a memristor but rather the more general class of memristive systems in which dx/dt exhibits an exponential rather than linear relationship with current. As far as I can tell there is STILL no solid state material which can legitimately be called a 2-terminal memristor as originally defined in Leon Chua’s 1971 paper.

Mouttet is quite wrong. There is no HP propaganda campaign to take credit for the memristor. HP Is not trying to impose an HP brand on the memristor idea.

Definition drift

Mouttet says Chua altered his definition of memristors to include "All 2-terminal non-volatile memory devices based on resistance switching," in a 2011 paper6. This meant his original memristor concept, HP's memristor devices and other technologies such as RRAM, PCM, and MRAM can all be called memristor-type technologies.

But previously, in his 1976 paper7, he had excluded such devices from being memristors, writing “...there remains an even broader class of physical devices and systems whose characteristics resemble those of the memristor and yet cannot be realistically modeled by this element...”

In Mouttet's judgment, "it appears that Chua has recently broadened the definition to save face for HP which has found that their device is not a memristor according to the original definition."

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