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

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Abstract

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.

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Acknowledgments

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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Authors and Affiliations

  1. Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian, 116024, China

    Lin Teng, Xingyuan Wang & Xiukun Wang

  2. School of Electrical, Electronic and Computer Engineering, The University of Western Australia, 35 Stirling Highway, Crawley, WA, 6009, Australia

    Herbert H. C. Iu

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  1. Lin Teng
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  2. Herbert H. C. Iu
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  3. Xingyuan Wang
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  4. Xiukun Wang
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Correspondence to Lin Teng or Xingyuan Wang.

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Teng, L., Iu, H.H.C., Wang, X. et al. Chaotic behavior in fractional-order memristor-based simplest chaotic circuit using fourth degree polynomial. Nonlinear Dyn 77, 231–241 (2014). https://doi.org/10.1007/s11071-014-1286-4

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  • DOI: https://doi.org/10.1007/s11071-014-1286-4

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