Nonlinear Dynamics

, Volume 70, Issue 2, pp 1185–1197 | Cite as

On the simplest fractional-order memristor-based chaotic system

  • Donato CafagnaEmail author
  • Giuseppe Grassi
Original Paper


In 1695, G. Leibniz laid the foundations of fractional calculus, but mathematicians revived it only 300 years later. In 1971, L.O. Chua postulated the existence of a fourth circuit element, called memristor, but Williams’s group of HP Labs realized it only 37 years later. By looking at these interdisciplinary and promising research areas, in this paper, a novel fractional-order system including a memristor is introduced. In particular, chaotic behaviors in the simplest fractional-order memristor-based system are shown. Numerical integrations (via a predictor–corrector method) and stability analysis of the system equilibria are carried out, with the aim to show that chaos can be found when the order of the derivative is 0.965. Finally, the presence of chaos is confirmed by the application of the recently introduced 0-1 test.


Fractional chaotic systems Chaotic attractors Noninteger-order dynamics Memristor 


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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Dipartimento Ingegneria InnovazioneUniversità del SalentoLecceItaly

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