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

Authors

  • Vanessa Avansini Botta Pirani
  • Cristiane Néspoli
  • Marcelo Messias

DOI:

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

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.

Downloads

Published

2011-06-01

How to Cite

Botta Pirani, V. A., Néspoli, C., & Messias, M. (2011). Mathematical Analisys of a Third-order Memristor-based Chua’s Oscillator. Trends in Computational and Applied Mathematics, 12(2), 91–99. https://doi.org/10.5540/tema.2011.012.02.0091

Issue

Vol. 12 No. 2 (2011)

Section

Original Article

License

Copyright

Authors of articles published in the journal Trends in Computational and Applied Mathematics retain the copyright of their work. The journal uses Creative Commons Attribution (CC-BY) in published articles. The authors grant the TCAM journal the right to first publish the article.

Intellectual Property and Terms of Use

The content of the articles is the exclusive responsibility of the authors. The journal uses Creative Commons Attribution (CC-BY) in published articles. This license allows published articles to be reused without permission for any purpose as long as the original work is correctly cited.

The journal encourages Authors to self-archive their accepted manuscripts, publishing them on personal blogs, institutional repositories, and social media, as long as the full citation is included in the journal's website version.