IDEAS home Printed from https://ideas.repec.org/a/wly/jnlamp/v2013y2013i1n657245.html

Nonlinear Dynamics and Chaos in Fractional‐Order Hopfield Neural Networks with Delay

Author

Listed:
  • Xia Huang
  • Zhen Wang
  • Yuxia Li

Abstract

A fractional‐order two‐neuron Hopfield neural network with delay is proposed based on the classic well‐known Hopfield neural networks, and further, the complex dynamical behaviors of such a network are investigated. A great variety of interesting dynamical phenomena, including single‐periodic, multiple‐periodic, and chaotic motions, are found to exist. The existence of chaotic attractors is verified by the bifurcation diagram and phase portraits as well.

Suggested Citation

  • Xia Huang & Zhen Wang & Yuxia Li, 2013. "Nonlinear Dynamics and Chaos in Fractional‐Order Hopfield Neural Networks with Delay," Advances in Mathematical Physics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlamp:v:2013:y:2013:i:1:n:657245
    DOI: 10.1155/2013/657245
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2013/657245
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2013/657245?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
    ---><---

    References listed on IDEAS

    as
    1. Lu, Jun Guo, 2005. "Chaotic dynamics and synchronization of fractional-order Arneodo’s systems," Chaos, Solitons & Fractals, Elsevier, vol. 26(4), pages 1125-1133.
    2. Chen, Wei-Ching, 2008. "Nonlinear dynamics and chaos in a fractional-order financial system," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1305-1314.
    3. Li, Chunguang & Chen, Guanrong, 2004. "Chaos and hyperchaos in the fractional-order Rössler equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 341(C), pages 55-61.
    4. Park, Ju H., 2006. "On global stability criterion for neural networks with discrete and distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 30(4), pages 897-902.
    5. Yu, Yongguang & Li, Han-Xiong & Wang, Sha & Yu, Junzhi, 2009. "Dynamic analysis of a fractional-order Lorenz chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1181-1189.
    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. Danca, Marius-F., 2021. "Hopfield neuronal network of fractional order: A note on its numerical integration," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).

    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. Jian Yuan & Bao Shi & Xiaoyun Zeng & Wenqiang Ji & Tetie Pan, 2013. "Sliding Mode Control of the Fractional‐Order Unified Chaotic System," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. Jian Yuan & Bao Shi & Wenqiang Ji, 2013. "Adaptive Sliding Mode Control of a Novel Class of Fractional Chaotic Systems," Advances in Mathematical Physics, John Wiley & Sons, vol. 2013(1).
    3. Deshpande, Amey S. & Daftardar-Gejji, Varsha, 2017. "On disappearance of chaos in fractional systems," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 119-126.
    4. Ge, Zheng-Ming & Yi, Chang-Xian, 2007. "Chaos in a nonlinear damped Mathieu system, in a nano resonator system and in its fractional order systems," Chaos, Solitons & Fractals, Elsevier, vol. 32(1), pages 42-61.
    5. 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 synchronization using optimized fractional order sli," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    6. Petráš, Ivo, 2008. "A note on the fractional-order Chua’s system," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 140-147.
    7. Silva-Juárez, Alejandro & Tlelo-Cuautle, Esteban & de la Fraga, Luis Gerardo & Li, Rui, 2021. "Optimization of the Kaplan-Yorke dimension in fractional-order chaotic oscillators by metaheuristics," Applied Mathematics and Computation, Elsevier, vol. 394(C).
    8. Xu, Fei & Lai, Yongzeng & Shu, Xiao-Bao, 2018. "Chaos in integer order and fractional order financial systems and their synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 125-136.
    9. Deepika, Deepika & Kaur, Sandeep & Narayan, Shiv, 2018. "Uncertainty and disturbance estimator based robust synchronization for a class of uncertain fractional chaotic system via fractional order sliding mode control," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 196-203.
    10. Baogui Xin & Yuting Li, 2013. "0‐1 Test for Chaos in a Fractional Order Financial System with Investment Incentive," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    11. Fei Gao & Xue-Jing Lee & Heng-qing Tong & Feng-xia Fei & Hua-ling Zhao, 2013. "Identification of Unknown Parameters and Orders via Cuckoo Search Oriented Statistically by Differential Evolution for Noncommensurate Fractional‐Order Chaotic Systems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    12. Khanzadeh, Alireza & Pourgholi, Mahdi, 2016. "Robust Synchronization of Fractional-Order Chaotic Systems at a Pre-Specified Time Using Sliding Mode Controller with Time-Varying Switching Surfaces," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 69-77.
    13. Lu, Jun Guo, 2006. "Synchronization of a class of fractional-order chaotic systems via a scalar transmitted signal," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 519-525.
    14. Ahmad, Shabir & Ullah, Aman & Akgül, Ali, 2021. "Investigating the complex behaviour of multi-scroll chaotic system with Caputo fractal-fractional operator," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    15. Munoz-Pacheco, J.M. & Zambrano-Serrano, E. & Volos, Ch. & Tacha, O.I. & Stouboulos, I.N. & Pham, V.-T., 2018. "A fractional order chaotic system with a 3D grid of variable attractors," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 69-78.
    16. Zhang, Weiwei & Zhou, Shangbo & Li, Hua & Zhu, Hao, 2009. "Chaos in a fractional-order Rössler system," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1684-1691.
    17. Gao, Yuan & Liang, Chenghua & Wu, Qiqi & Yuan, Haiying, 2015. "A new fractional-order hyperchaotic system and its modified projective synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 76(C), pages 190-204.
    18. Hajipour, Ahamad & Hajipour, Mojtaba & Baleanu, Dumitru, 2018. "On the adaptive sliding mode controller for a hyperchaotic fractional-order financial system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 497(C), pages 139-153.
    19. Das, Saptarshi & Pan, Indranil & Das, Shantanu, 2016. "Effect of random parameter switching on commensurate fractional order chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 157-173.
    20. Ge, Zheng-Ming & Ou, Chan-Yi, 2007. "Chaos in a fractional order modified Duffing system," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 262-291.

    More about this item

    Statistics

    Access and download statistics

    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:wly:jnlamp:v:2013:y:2013:i:1:n:657245. 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: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/3197 .

    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.