Sah, Maheshwar Prasad; Mannan, Zubaer Ibna; Kim, Hyongsuk; Chua, Leon Oscillator made of only one memristor and one battery. (English) Zbl 1314.94117 Int. J. Bifurcation Chaos Appl. Sci. Eng. 25, No. 3, Article ID 1530010, 28 p. (2015). 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. Cited in 8 Documents 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 Keywords:memristor; pinched hysteresis loop; oscillator; local activity; edge of chaos; super-critical Hopf-bifurcation PDFBibTeX XMLCite \textit{M. P. Sah} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 25, No. 3, Article ID 1530010, 28 p. (2015; Zbl 1314.94117) Full Text: DOI References: [1] DOI: 10.1109/TCSI.2013.2256171 · doi:10.1109/TCSI.2013.2256171 [2] Chua L. O., Introduction to Nonlinear Network Theory (1969) [3] DOI: 10.1109/PROC.1976.10092 · doi:10.1109/PROC.1976.10092 [4] Chua L. O., Linear and Nonlinear Circuits (1987) · Zbl 0631.94017 [5] DOI: 10.1142/9789812798589 · doi:10.1142/9789812798589 [6] DOI: 10.1109/JPROC.2003.818319 · doi:10.1109/JPROC.2003.818319 [7] Chua L., Int. J. Bifurcation and Chaos 22 pp 1230011-1– (2012) [8] Chua L., Int. J. Bifurcation and Chaos 22 pp 1250098-1– (2012) [9] DOI: 10.1088/0268-1242/29/10/104001 · doi:10.1088/0268-1242/29/10/104001 [10] DOI: 10.1142/S0218127498000152 · Zbl 0933.37042 · doi:10.1142/S0218127498000152 [11] Mehta V. K., Principle of Electronics (2005) [12] DOI: 10.1137/1.9780898718232 · doi:10.1137/1.9780898718232 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.