Mathematical Analisys of a Third-order Memristor-based Chua's Oscillator

Vanessa Avansini Botta Pirani, Cristiane Néspoli, Marcelo Messias

Abstract


Abstract. In this paper we present a detailed linear analysis of the equilibrium points stability of a memristor oscillator mathematical model, given by a threedimensional 5-parameter piecewise-linear system of ordinary differential equations. We perform the linear analysis in the general case and present numerical simulations for some particular parameter values.

References


[1] L.O. Chua, Memristor – the missing circuit element, IEEE Trans. Circuit Th. 18 (1971), 507–519.

[2] B. Fiedler, S. Liebscher, J.C. Alexander, Generic Hopf bifurcation from lines of equilibria without parameters: I. Theory, J. Differential Equations 167 (2000), 16–35.

[3] M. Hopkin, Found: the missing circuit element, Nature News, April 2008.

[4] M. Itoh, L.O. Chua, Memristor oscillators, Internat. J. Bifur. Chaos Appl. Sci. Engrg, 18 (2008), 3183–3206.

[5] M. Messias, C. Nespoli, V.A. Botta, Hopf bifurcation from lines of equilibria without parameters in memristor oscillators, Internat. J. Bifur. Chaos Appl. Sci. Engrg 20 (2010) 437–450.

[6] D.B. Strukov, G.S. Snider, G.R. Stewart, R.S.Williams, The missing menristor found, Nature 453 (2008), 80–83.




DOI: https://doi.org/10.5540/tema.2011.012.02.0091

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Trends in Computational and Applied Mathematics

A publication of the Brazilian Society of Applied and Computational Mathematics (SBMAC)

 

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