Abstract
This paper explains why charge- and flux-controlled memristor dynamics comply with Bernoulli's nonlinear differential equation. These devices are termed Bernoulli memristors. Based on the fact that their identified nonlinear dynamics can always be treated in a linearized manner, a general mathematical framework suitable for the systematic study of individual or networks of Bernoulli memristors can be developed. The paper details the novel mathematical framework and showcases its usefulness: 1) by applying it to obtain a closed-form expression of the output as an explicit function of the input for an example memristor model whose dynamics are described by a power law; 2) by determining analytically the harmonic content of the output of a Bernoulli memristor driven by a sinewave; 3) by investigating systematically the dynamics of networks of Bernoulli memristors connected either in series or in parallel; and 4) by assessing qualitatively the impact of series parasitic ohmic resistance on the dynamics of an ideal memristor.
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