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Oscillator made of only one memristor and one battery. (English) Zbl 1314.94117

Summary: Contrary to the traditional belief that at least two energy-storage elements (capacitor and/or inductor) and a locally-active nonlinearity are needed to build an electronic oscillator, this paper presents an oscillator made with only two circuit elements, namely, a memristor and a battery. This simplest of all physical oscillators also serves as a textbook example for explaining the intimate relationship between the super-critical Hopf bifurcation phenomenon and the edge of chaos.

MSC:

94C05 Analytic circuit theory
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
34C23 Bifurcation theory for ordinary differential equations
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