IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v92y2016icp20-29.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077916302648
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2016.09.013?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Zhiqin Qiao & Xianyi Li, 2014. "Dynamical analysis and numerical simulation of a new Lorenz-type chaotic system," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 20(3), pages 264-283, May.
    2. Ma, Yingjie & Li, Ya & Jiang, Xiling, 2015. "Simulation and circuit implementation of 12-scroll chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 75(C), pages 127-133.
    3. Dmitri B. Strukov & Gregory S. Snider & Duncan R. Stewart & R. Stanley Williams, 2008. "The missing memristor found," Nature, Nature, vol. 453(7191), pages 80-83, May.
    4. Qi, Guoyuan & Chen, Guanrong & Du, Shengzhi & Chen, Zengqiang & Yuan, Zhuzhi, 2005. "Analysis of a new chaotic system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 352(2), pages 295-308.
    5. Qi, Guoyuan & van Wyk, Michaël Antonie & van Wyk, Barend Jacobus & Chen, Guanrong, 2009. "A new hyperchaotic system and its circuit implementation," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2544-2549.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Xin, Zeng-Jun & Lai, Qiang, 2024. "Dynamical investigation and encryption application of a new multiscroll memristive chaotic system with rich offset boosting features," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    2. Lai, Qiang & Chen, Zhijie, 2023. "Grid-scroll memristive chaotic system with application to image encryption," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    3. Ahmad Taher Azar & Christos Volos & Nikolaos A. Gerodimos & George S. Tombras & Viet-Thanh Pham & Ahmed G. Radwan & Sundarapandian Vaidyanathan & Adel Ouannas & Jesus M. Munoz-Pacheco, 2017. "A Novel Chaotic System without Equilibrium: Dynamics, Synchronization, and Circuit Realization," Complexity, Hindawi, vol. 2017, pages 1-11, February.
    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. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Feng, Liang & Hu, Cheng & Yu, Juan & Jiang, Haijun & Wen, Shiping, 2021. "Fixed-time Synchronization of Coupled Memristive Complex-valued Neural Networks," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    2. Liang, Xiyin & Qi, Guoyuan, 2017. "Mechanical analysis of Chen chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 98(C), pages 173-177.
    3. Hu, Yongbing & Li, Qian & Ding, Dawei & Jiang, Li & Yang, Zongli & Zhang, Hongwei & Zhang, Zhixin, 2021. "Multiple coexisting analysis of a fractional-order coupled memristive system and its application in image encryption," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    4. Zhang, Ge & Ma, Jun & Alsaedi, Ahmed & Ahmad, Bashir & Alzahrani, Faris, 2018. "Dynamical behavior and application in Josephson Junction coupled by memristor," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 290-299.
    5. Dong, Chengwei & Yang, Min & Jia, Lian & Li, Zirun, 2024. "Dynamics investigation and chaos-based application of a novel no-equilibrium system with coexisting hidden attractors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 633(C).
    6. Wu, Wen-Juan & Chen, Zeng-Qiang & Yuan, Zhu-Zhi, 2009. "A computer-assisted proof for the existence of horseshoe in a novel chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2756-2761.
    7. Ghamati, Mina & Balochian, Saeed, 2015. "Design of adaptive sliding mode control for synchronization Genesio–Tesi chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 75(C), pages 111-117.
    8. Qin, Xiaoli & Wang, Cong & Li, Lixiang & Peng, Haipeng & Yang, Yixian & Ye, Lu, 2018. "Finite-time modified projective synchronization of memristor-based neural network with multi-links and leakage delay," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 302-315.
    9. Ui Yeon Won & Quoc An Vu & Sung Bum Park & Mi Hyang Park & Van Dam Do & Hyun Jun Park & Heejun Yang & Young Hee Lee & Woo Jong Yu, 2023. "Multi-neuron connection using multi-terminal floating–gate memristor for unsupervised learning," Nature Communications, Nature, vol. 14(1), pages 1-11, December.
    10. Lijuan Chen & Mingchu Yu & Jinnan Luo & Jinpeng Mi & Kaibo Shi & Song Tang, 2024. "Dynamic Analysis and FPGA Implementation of a New Linear Memristor-Based Hyperchaotic System with Strong Complexity," Mathematics, MDPI, vol. 12(12), pages 1-17, June.
    11. Laarem, Guessas, 2021. "A new 4-D hyper chaotic system generated from the 3-D Rösslor chaotic system, dynamical analysis, chaos stabilization via an optimized linear feedback control, it’s fractional order model and chaos sy," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    12. Liu, Yunfeng & Song, Zhiqiang & Tan, Manchun, 2019. "Multiple μ-stability and multiperiodicity of delayed memristor-based fuzzy cellular neural networks with nonmonotonic activation functions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 159(C), pages 1-17.
    13. Kwon, Osung & Kim, Sungjun & Agudov, Nikolay & Krichigin, Alexey & Mikhaylov, Alexey & Grimaudo, Roberto & Valenti, Davide & Spagnolo, Bernardo, 2022. "Non-volatile memory characteristics of a Ti/HfO2/Pt synaptic device with a crossbar array structure," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    14. Deng, Yue & Li, Yuxia, 2021. "Bifurcation and bursting oscillations in 2D non-autonomous discrete memristor-based hyperchaotic map," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    15. 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).
    16. Aguilera-Morillo, M. Carmen & Aguilera, Ana M. & Jiménez-Molinos, Francisco & Roldán, Juan B., 2019. "Stochastic modeling of Random Access Memories reset transitions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 159(C), pages 197-209.
    17. Jahanshahi, Hadi & Yousefpour, Amin & Munoz-Pacheco, Jesus M. & Kacar, Sezgin & Pham, Viet-Thanh & Alsaadi, Fawaz E., 2020. "A new fractional-order hyperchaotic memristor oscillator: Dynamic analysis, robust adaptive synchronization, and its application to voice encryption," Applied Mathematics and Computation, Elsevier, vol. 383(C).
    18. Filatov, D.O. & Koryazhkina, M.N. & Novikov, A.S. & Shishmakova, V.A. & Shenina, M.E. & Antonov, I.N. & Gorshkov, O.N. & Agudov, N.V. & Carollo, A. & Valenti, D. & Spagnolo, B., 2022. "Effect of internal noise on the relaxation time of an yttria stabilized zirconia-based memristor," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    19. Dong, Yujiao & Yang, Shuting & Liang, Yan & Wang, Guangyi, 2022. "Neuromorphic dynamics near the edge of chaos in memristive neurons," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    20. Konlechner, Roland & Allagui, Anis & Antonov, Vladimir N. & Yudin, Dmitry, 2023. "A superstatistics approach to the modelling of memristor current–voltage responses," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 614(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:92:y:2016:i:c:p:20-29. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.