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A Hyperjerk Memristive System with Hidden Attractors

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Advances in Memristors, Memristive Devices and Systems

Part of the book series: Studies in Computational Intelligence ((SCI,volume 701))

Abstract

After the introduction by Leonov and Kuznetsov of a new classification of nonlinear dynamics with kinds of attractors (self-excited attractors and hidden attractors), this subject has received a significant interest. From an engineering point of view, hidden attractors are important and can lead to unexpected behavior. Various chaotic systems with the presence of hidden attractors have been discovered recently. Especially, memristor, the fourth basic circuit element, can be used to construct such chaotic systems. This chapter presents a new memristive system which can display hidden chaotic attractor. Interestingly, this memristive system is a hyperjerk system because it involves time derivatives of a jerk function. The fundamental dynamics properties of such memristive system are discovered by calculating the number of equilibrium points, using phase portraits, Poincaré map, bifurcation diagram, maximum Lyapunov exponents, and Kaplan–Yorke fractional dimension. Also, we have investigated the multi–stability in the memristive system by varying the value of its initial condition. In addition, adaptive synchronization for the hyperjerk memristive system is also studied. The proposed memristive system can be applied into chaos–based engineering applications because of its chaotic behavior.

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Acknowledgements

The author Xiong Wang was supported by the National Natural Science Foundation of China (No. 61601306) and Shenzhen Overseas High Level Talent Peacock Project Fund (No. 20150215145C). V.-T. Pham is grateful to Le Thi Van Thu, Philips Electronics—Vietnam, for her help.

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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, Chennai, Tamil Nadu, India

    Sundarapandian Vaidyanathan

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

    Christos Volos

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

    Xiong Wang

  5. Ton Duc Thang University, Ho Chi Minh, Vietnam

    Duy Vo Hoang

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  1. Viet-Thanh Pham
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  2. Sundarapandian Vaidyanathan
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  3. Christos Volos
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  4. Xiong Wang
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  5. Duy Vo Hoang
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Correspondence to Viet-Thanh Pham .

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Editors and Affiliations

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

    Sundarapandian Vaidyanathan

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

    Christos Volos

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Pham, VT., Vaidyanathan, S., Volos, C., Wang, X., Hoang, D.V. (2017). A Hyperjerk Memristive System with Hidden Attractors. In: Vaidyanathan, S., Volos, C. (eds) Advances in Memristors, Memristive Devices and Systems. Studies in Computational Intelligence, vol 701. Springer, Cham. https://doi.org/10.1007/978-3-319-51724-7_3

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