IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v146y2021ics0960077921002678.html
   My bibliography  Save this article

Analysis of basins of attraction of new coupled hidden attractor system

Author

Listed:
  • Cui, Li
  • Luo, Wenhui
  • Ou, Qingli

Abstract

This paper mainly discusses the characteristic of the basin of attraction of two coupled chaotic systems, which provides a theoretical basis for the application of nonlinear systems in the fields of communication, control and artificial intelligence. Thus, in order to increase the complexity of the chaotic systems, two identical linear couplings are used to hide a system composed of attractors, and therefore the system has chaotic characteristic within a specific coupling strength range. We use an ode45 algorithm to solve the coupled chaotic systems to obtain a chaotic phase diagram, Lyaponov exponential spectrum and a bifurcation diagram of the system and prove that the attractors of the coupled systems are attractors in the sense of Milnor, and the basin of attraction of the coupled chaotic systems has a sieve-type property. A Lyaponov exponential function of the nonlinear system can be used to analyze the stability of the system, when the system operates in an initial state, the system will move in the direction that the Lyaponov exponential function decreases until it reaches a local minimum, a local minimum point of the Lyaponov exponential function represents a stable point of a phase space, and each attractor surrounds one substantial basin of attraction. Therefore, we use a Lyaponov exponent to describe and analyze the basin of attraction of the coupled chaotic systems. And meanwhile, when analyzing the system, we found that the system has rich dynamic behavior and multi-stability for hiding of the attractors.

Suggested Citation

  • Cui, Li & Luo, Wenhui & Ou, Qingli, 2021. "Analysis of basins of attraction of new coupled hidden attractor system," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    • Handle: RePEc:eee:chsofr:v:146:y:2021:i:c:s0960077921002678
    DOI: 10.1016/j.chaos.2021.110913
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077921002678
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2021.110913?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. Kim, Jinhyon & Ju, Hyonhui, 2018. "Hausdorff dimension of the sets of Li-Yorke pairs for some chaotic dynamical systems including A-coupled expanding systems," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 246-251.
    2. Cui, Li & Lu, Ming & Ou, Qingli & Duan, Hao & Luo, Wenhui, 2020. "Analysis and Circuit Implementation of Fractional Order Multi-wing Hidden Attractors," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    3. Jiang, Congshi & Chen, Quan, 2020. "Construction of blind restoration model for super-resolution image based on chaotic neural network," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    4. Falcão, M. Irene & Miranda, Fernando & Severino, Ricardo & Soares, M. Joana, 2017. "Basins of attraction for a quadratic coquaternionic map," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 716-724.
    5. Durdu, Ali & Uyaroğlu, Yılmaz, 2017. "The Shortest Synchronization Time with Optimal Fractional Order Value Using a Novel Chaotic Attractor Based on Secure Communication," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 98-106.
    6. Pavlov, A.N. & Pavlova, O.N. & Koronovskii, A.A. & Hramov, A.E., 2018. "Effect of measuring noise on scaling characteristics in the dynamics of coupled chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 106-113.
    7. Pavlova, O.N. & Pavlov, A.N., 2020. "Prediction of complex oscillations in the dynamics of coupled chaotic systems using transients," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    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. Ma, Tao & Mou, Jun & Banerjee, Santo & Cao, Yinghong, 2023. "Analysis of the functional behavior of fractional-order discrete neuron under electromagnetic radiation," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    2. Liang, Bo & Hu, Chenyang & Tian, Zean & Wang, Qiao & Jian, Canling, 2023. "A 3D chaotic system with multi-transient behavior and its application in image encryption," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 616(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. Luo, Shaohua & Yang, Guanci & Li, Junyang & Ouakad, Hassen M., 2022. "Dynamic analysis, circuit realization and accelerated adaptive backstepping control of the FO MEMS gyroscope," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    2. Bashkirtseva, Irina A. & Ryashko, Lev B. & Pisarchik, Alexander N., 2020. "Ring of map-based neural oscillators: From order to chaos and back," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    3. Sahoo, Shilalipi & Roy, Binoy Krishna, 2022. "Design of multi-wing chaotic systems with higher largest Lyapunov exponent," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    4. Durdu, Ali & Uyaroğlu, Yılmaz, 2022. "Comparison of synchronization of chaotic Burke-Shaw attractor with active control and integer-order and fractional-order P-C method," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    5. Ben-Loghfyry, Anouar & Charkaoui, Abderrahim, 2023. "Regularized Perona & Malik model involving Caputo time-fractional derivative with application to image denoising," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    6. Sahoo, Shilalipi & Roy, Binoy Krishna, 2022. "A new multi-wing chaotic attractor with unusual variation in the number of wings," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    7. Chenchen Peng & Haiyi Yang & Anqing Yang & Ling Ren, 2024. "A New Observer Design for the Joint Estimation of States and Unknown Inputs for a Class of Nonlinear Fractional-Order Systems," Mathematics, MDPI, vol. 12(8), pages 1-12, April.
    8. Fei Yu & Shuai Xu & Yue Lin & Ting He & Chaoran Wu & Hairong Lin, 2024. "Design and Analysis of a Novel Fractional-Order System with Hidden Dynamics, Hyperchaotic Behavior and Multi-Scroll Attractors," Mathematics, MDPI, vol. 12(14), pages 1-22, July.
    9. Tutueva, Aleksandra V. & Moysis, Lazaros & Rybin, Vyacheslav G. & Kopets, Ekaterina E. & Volos, Christos & Butusov, Denis N., 2022. "Fast synchronization of symmetric Hénon maps using adaptive symmetry control," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    10. Junrong Guo & Xiaolin Liu & Ping Yan, 2023. "Dynamic Analysis of Impulsive Differential Chaotic System and Its Application in Image Encryption," Mathematics, MDPI, vol. 11(23), pages 1-18, November.
    11. Cang, Shijian & Zhao, Gehang & Wang, Zenghui & Chen, Zengqiang, 2022. "Global structures of clew-shaped conservative chaotic flows in a class of 3D one-thermostat systems," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    12. Anguiano-Gijón, Carlos Alberto & Muñoz-Vázquez, Aldo Jonathan & Sánchez-Torres, Juan Diego & Romero-Galván, Gerardo & Martínez-Reyes, Fernando, 2019. "On predefined-time synchronisation of chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 172-178.

    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:146:y:2021:i:c:s0960077921002678. 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.