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A Chaotic Hyperjerk System Based on Memristive Device

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Advances and Applications in Chaotic Systems

Part of the book series: Studies in Computational Intelligence ((SCI,volume 636))

Abstract

From the mechanical system point of view, third-order derivatives of displacement or the time rate of change of acceleration is the jerk, while the fourth derivative has been known as a snap. As a result, a dynamical system which is presented by an nth order ordinary differential equation with \( n > 3 \) describing the time evolution of a single scalar variable is considered as a hyperjerk system. Hyperjerk system has received significant attention because of its elegant form. Motivated by reported attractive hyperjerk systems, a 4-D novel chaotic hyperjerk system has been introduced and studied in this work. Interestingly, this hyperjerk system displays an infinite number of equilibrium points because of the presence of a memristive device. In addition, an adaptive controller is proposed to achieve synchronization of such novel hyperjerk systems with two unknown parameters. In order to confirm the feasibility of the mathematical hyperjerk model, its electronic circuit is designed and implemented by using SPICE.

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Acknowledgments

This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 102.99–2013.06.

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Authors and Affiliations

  1. School of Electronics and Telecommunications, Hanoi University of Science and Technology, Hanoi, Vietnam

    Viet-Thanh Pham

  2. Research and Development Centre, Vel Tech University, Tamil Nadu, India

    Sundarapandian Vaidyanathan

  3. Physics Department, Aristotle University of Thessaloniki, Thessaloniki, Greece

    Christos K. Volos

  4. Biomedical Engineering Faculty, Amirkabir University of Technology, Tehran, Iran

    Sajad Jafari

  5. Institute for Advanced Study, Shenzhen University, Guangdong, Shenzhen, 518060, People’s Republic of China

    Xiong Wang

Authors
  1. Viet-Thanh Pham
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  2. Sundarapandian Vaidyanathan
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  3. Christos K. Volos
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  4. Sajad Jafari
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  5. Xiong Wang
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Correspondence to Viet-Thanh Pham .

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Editors and Affiliations

  1. Research and Development Centre, Vel Tech University, Chennai, India

    Sundarapandian Vaidyanathan

  2. Department of Physics, Aristotle University of Thessaloniki, Thessaloniki, Greece

    Christos Volos

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Pham, VT., Vaidyanathan, S., Volos, C.K., Jafari, S., Wang, X. (2016). A Chaotic Hyperjerk System Based on Memristive Device. In: Vaidyanathan, S., Volos, C. (eds) Advances and Applications in Chaotic Systems . Studies in Computational Intelligence, vol 636. Springer, Cham. https://doi.org/10.1007/978-3-319-30279-9_2

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  • DOI: https://doi.org/10.1007/978-3-319-30279-9_2

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