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Quasi-pinning synchronization and stabilization of fractional order BAM neural networks with delays and discontinuous neuron activations

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  • Pratap, A.
  • Raja, R.
  • Cao, J.
  • Rihan, Fathalla A.
  • Seadawy, Aly R.

Abstract

This manuscript concerns quasi-pinning synchronization and β-exponential pinning stabilization for a class of fractional order BAM neural networks with time-varying delays and discontinuous neuron activations (FBAMNNDDAs). Firstly, under the framework of Filippov solution and fractional-order differential inclusions analysis for the initial value problem of FBAMNNDDAs is presented. Secondly, two kinds of novel pinning controllers according to pinning control technique are designed. By means of fractional order Lyapunov method and designed pinning control strategy, the sufficient criteria is given first to ensure the quasi-synchronization for the dynamic behavior of FBAMNNDDAs. Furthermore, the error bound of pinning synchronization is explicitly evaluated. Thirdly, via Kakutani s fixed point theorem of set-valued map analysis, Razumikhin condition, and a nonlinear pinning controller, the existence and β-exponential stabilization of FBAMNNDDAs equilibrium point is obtained in the voice of linear matrix inequality (LMI) technique. Fourthly, based on as well as Mittag-Leffler function and growth condition, the global existence of a solution in the Filippov sense of such system is guaranteed with detailed proof. At last, a numerical example with computer simulations are performed to illustrate the effectiveness of proposed theoretical consequences.

Suggested Citation

  • Pratap, A. & Raja, R. & Cao, J. & Rihan, Fathalla A. & Seadawy, Aly R., 2020. "Quasi-pinning synchronization and stabilization of fractional order BAM neural networks with delays and discontinuous neuron activations," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    • Handle: RePEc:eee:chsofr:v:131:y:2020:i:c:s0960077919304370
    DOI: 10.1016/j.chaos.2019.109491
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    1. Hongguang Fan & Yue Rao & Kaibo Shi & Hui Wen, 2023. "Global Synchronization of Fractional-Order Multi-Delay Coupled Neural Networks with Multi-Link Complicated Structures via Hybrid Impulsive Control," Mathematics, MDPI, vol. 11(14), pages 1-17, July.
    2. Xu, Changjin & Liu, Zixin & Yao, Lingyun & Aouiti, Chaouki, 2021. "Further exploration on bifurcation of fractional-order six-neuron bi-directional associative memory neural networks with multi-delays," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    3. Usa Humphries & Grienggrai Rajchakit & Pramet Kaewmesri & Pharunyou Chanthorn & Ramalingam Sriraman & Rajendran Samidurai & Chee Peng Lim, 2020. "Global Stability Analysis of Fractional-Order Quaternion-Valued Bidirectional Associative Memory Neural Networks," Mathematics, MDPI, vol. 8(5), pages 1-27, May.
    4. Kashkynbayev, Ardak & Cao, Jinde & Suragan, Durvudkhan, 2021. "Global Lagrange stability analysis of retarded SICNNs," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    5. Xu, Changjin & Liu, Zixin & Liao, Maoxin & Li, Peiluan & Xiao, Qimei & Yuan, Shuai, 2021. "Fractional-order bidirectional associate memory (BAM) neural networks with multiple delays: The case of Hopf bifurcation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 471-494.
    6. Wang, Shuzhan & Zhang, Ziye & Lin, Chong & Chen, Jian, 2021. "Fixed-time synchronization for complex-valued BAM neural networks with time-varying delays via pinning control and adaptive pinning control," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    7. Gani Stamov & Ivanka Stamova & Stanislav Simeonov & Ivan Torlakov, 2020. "On the Stability with Respect to H-Manifolds for Cohen–Grossberg-Type Bidirectional Associative Memory Neural Networks with Variable Impulsive Perturbations and Time-Varying Delays," Mathematics, MDPI, vol. 8(3), pages 1-14, March.
    8. Alsaedi, Ahmed & Cao, Jinde & Ahmad, Bashir & Alshehri, Ahmed & Tan, Xuegang, 2022. "Synchronization of master-slave memristive neural networks via fuzzy output-based adaptive strategy," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    9. Mahmoudabadi, Parvin & Tavakoli-Kakhki, Mahsan, 2021. "Tracking control with disturbance rejection of nonlinear fractional order fuzzy systems: Modified repetitive control approach," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    10. Stamov, Gani & Stamova, Ivanka & Martynyuk, Anatoliy & Stamov, Trayan, 2021. "Almost periodic dynamics in a new class of impulsive reaction–diffusion neural networks with fractional-like derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    11. Zhang, Xiulan & Liu, YiYu & Qiu, Hongling & Liu, Heng, 2024. "Dissipativity and synchronization of fractional-order output-coupled neural networks with multiple adaptive coupling weights," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 215(C), pages 306-322.
    12. Zhen Yang & Zhengqiu Zhang, 2022. "Finite-Time Synchronization Analysis for BAM Neural Networks with Time-Varying Delays by Applying the Maximum-Value Approach with New Inequalities," Mathematics, MDPI, vol. 10(5), pages 1-16, March.

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