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Non-Smooth Bifurcation in Two Fractional-Order Memristive Circuits

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New Trends in Nonlinear Dynamics

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Abstract

Two fractional-order Chua’s memristive circuits named Model 1 and Model 2 are proposed. Model 1 is a fractional-order memristive circuit with only the memristor described by a fractional-order derivative due to the memory loss observed experimentally, while Model 2 is a direct fractional-order generalization of integer-order Chua’s memristive circuit without considering the physical background. Both models are non-smooth systems with a line equilibrium depending on the memristor’s initial state. Numerical simulation shows that both models exhibit multi-stability and different steady states switch via “grazing bifurcation” or “tangent bifurcation,” “intermittent chaos” is found in Model 1 as the fractional order is close to 0 or 1, but no “intermittent chaos” is found in Model 2 as the fractional order is between 0 and 1.

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Acknowledgement

This work was supported by Natural Science Foundation of China under Grants 11602035 and 11372354.

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Authors and Affiliations

  1. School of Mathematics and Physics, Changzhou University, Changzhou, China

    Yajuan Yu

  2. State Key Lab of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing, China

    Zaihua Wang

Authors
  1. Yajuan Yu
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  2. Zaihua Wang
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Corresponding author

Correspondence to Zaihua Wang .

Editor information

Editors and Affiliations

  1. Department of Structural and Geotechnical Engineering, Sapienza University of Rome, Rome, Italy

    Walter Lacarbonara

  2. Department of Mechanical Engineering, University of Maryland, College Park, MD, USA

    Balakumar Balachandran

  3. Department of Physics, Lanzhou University of Technology, Lanzhou, Gansu, China

    Jun Ma

  4. Department of Electrical Engineering, Polytechnic of Porto - School of Engineering (ISEP), Porto, Portugal

    J. A. Tenreiro Machado

  5. Department of Applied Mechanics, Budapest University of Technology and Economics, Budapest, Hungary

    Gabor Stepan

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Yu, Y., Wang, Z. (2020). Non-Smooth Bifurcation in Two Fractional-Order Memristive Circuits. In: Lacarbonara, W., Balachandran, B., Ma, J., Tenreiro Machado, J., Stepan, G. (eds) New Trends in Nonlinear Dynamics. Springer, Cham. https://doi.org/10.1007/978-3-030-34724-6_33

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