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Analysis of basins of attraction of new coupled hidden attractor system

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  • 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
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    References listed on IDEAS

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    1. 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).
    2. 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.
    3. 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.
    4. 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.
    5. 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).
    6. 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.
    7. 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).
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    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).

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