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A memristive chaotic system with heart-shaped attractors and its implementation

Author

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  • Wu, Jiening
  • Wang, Lidan
  • Chen, Guanrong
  • Duan, Shukai

Abstract

As a controllable nonlinear element, memristor is easy to produce the chaotic signal. Most of the current researchers focus on the nonlinear characteristics of the memristor, however, its ability to control and adjust chaotic systems is often neglected. Therefore, a memristive chaotic system is introduced to generate a kind of heart-shaped attractors in this paper. To further understand the complex dynamics of the system, several basic dynamical behavior of the new chaotic system, such as dissipation and the stability of the equilibrium point is investigated. Some basic properties such as Poincaré-map, Lyapunov index and bifurcation diagram are presented, either analytically or numerically. In addition, the influence of parameters on the system's dynamic behavior is analyzed. Finally, an analog implementation based on PSPICE simulation is also designed. The obtained results clearly show this chaotic system has rich nonlinear characteristics. Some interesting conclusions can be drawn that memristors bring the following effects on chaotic systems: (a) when the polarity of the memristor is changed, a mirror image of the chaotic attractors will appeared in the system; (b) along with the proper choose of the memristor parameters, the chaotic motion of system will be suppressed and enhanced, which makes the system can be applied to the practice on either generating chaos signal or suppressing chaotic interference.

Suggested Citation

  • Wu, Jiening & Wang, Lidan & Chen, Guanrong & Duan, Shukai, 2016. "A memristive chaotic system with heart-shaped attractors and its implementation," Chaos, Solitons & Fractals, Elsevier, vol. 92(C), pages 20-29.
    • Handle: RePEc:eee:chsofr:v:92:y:2016:i:c:p:20-29
    DOI: 10.1016/j.chaos.2016.09.013
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    References listed on IDEAS

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    Cited by:

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    4. Rodrigo Méndez-Ramírez & Adrian Arellano-Delgado & César Cruz-Hernández & Rigoberto Martínez-Clark, 2017. "A New Simple Chaotic Lorenz-Type System and Its Digital Realization Using a TFT Touch-Screen Display Embedded System," Complexity, Hindawi, vol. 2017, pages 1-13, July.
    5. Ma, Xujiong & Mou, Jun & Xiong, Li & Banerjee, Santo & Cao, Yinghong & Wang, Jieyang, 2021. "A novel chaotic circuit with coexistence of multiple attractors and state transition based on two memristors," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    6. Bo Wang, 2019. "Results on a Novel Piecewise-Linear Memristor-Based Chaotic System," Complexity, Hindawi, vol. 2019, pages 1-6, January.
    7. Zhang, Lingshuang & Li, Zhijun & Peng, Yuexi, 2024. "A hidden grid multi-scroll chaotic system coined with two multi-stable memristors," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).
    8. Hairong Lin & Chunhua Wang & Fei Yu & Jingru Sun & Sichun Du & Zekun Deng & Quanli Deng, 2023. "A Review of Chaotic Systems Based on Memristive Hopfield Neural Networks," Mathematics, MDPI, vol. 11(6), pages 1-18, March.

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