Nonlinear Dynamics

, Volume 77, Issue 1–2, pp 231–241 | Cite as

Chaotic behavior in fractional-order memristor-based simplest chaotic circuit using fourth degree polynomial

  • Lin TengEmail author
  • Herbert H. C. Iu
  • Xingyuan WangEmail author
  • Xiukun Wang
Original Paper


In this paper, a memristor with a fourth degree polynomial memristance function is used in the simplest chaotic circuit which has only three circuit elements: a linear passive inductor, a linear passive capacitor, and a nonlinear active memristor. We use second order exponent internal state memristor function and fourth degree polynomial memristance function to increase complexity of the chaos. So, the system can generate double-scroll attractor and four-scroll attractor. Systematic studies of chaotic behavior in the integer-order and fractional-order systems are performed using phase portraits, bifurcation diagrams, Lyapunov exponents, and stability analysis. Simulation results show that both integer-order and fractional-order systems exhibit chaotic behavior over a range of control parameters.


Chaos Fractional-order system Memristor Simplest chaotic circuit 



This research is supported by the National Natural Science Foundation of China (Nos: 61370145, 61173183, and 60973152), the Doctoral Program Foundation of Institution of Higher Education of China (No: 20070141014), Program for Liaoning Excellent Talents in University (No: LR2012003), the National Natural Science Foundation of Liaoning province (No: 20082165), and the Fundamental Research Funds for the Central Universities (No: DUT12JB06). The authors gratefully acknowledge the China Scholarship Council for providing L. Teng a postgraduate scholarship.


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Faculty of Electronic Information and Electrical EngineeringDalian University of TechnologyDalianChina
  2. 2.School of Electrical, Electronic and Computer EngineeringThe University of Western AustraliaCrawleyAustralia

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