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Exponential and fixed-time synchronization of Cohen–Grossberg neural networks with time-varying delays and reaction-diffusion terms

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  • Li, Ruoxia
  • Cao, Jinde
  • Alsaedi, Ahmad
  • Alsaadi, Fuad

Abstract

This paper is devoted to the global exponential and fixed-time synchronization of delayed reaction-diffusion Cohen–Grossberg neural networks. Adaptive controllers are designed such that the addressed system can realize global exponential synchronization goal under the framework of inequality techniques, Lyapunov method as well as some suitable assumptions. Furthermore, as corollaries, the corresponding conclusion is provided to ensure the delayed Cohen–Grossberg neural networks without reaction-diffusion term can reach fixed-time synchronization goal. In addition, the settling time of fixed-time synchronization can be adjusted to desired values regardless of initial conditions, which is more reasonable. Finally, two numerical examples and its simulations are given to show the effectiveness of the obtained results.

Suggested Citation

  • Li, Ruoxia & Cao, Jinde & Alsaedi, Ahmad & Alsaadi, Fuad, 2017. "Exponential and fixed-time synchronization of Cohen–Grossberg neural networks with time-varying delays and reaction-diffusion terms," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 37-51.
    • Handle: RePEc:eee:apmaco:v:313:y:2017:i:c:p:37-51
    DOI: 10.1016/j.amc.2017.05.073
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    References listed on IDEAS

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    1. Bao, Haibo & Park, Ju H. & Cao, Jinde, 2015. "Matrix measure strategies for exponential synchronization and anti-synchronization of memristor-based neural networks with time-varying delays," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 543-556.
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    3. Rajavel, S. & Samidurai, R. & Cao, Jinde & Alsaedi, Ahmed & Ahmad, Bashir, 2017. "Finite-time non-fragile passivity control for neural networks with time-varying delay," Applied Mathematics and Computation, Elsevier, vol. 297(C), pages 145-158.
    4. Li, Ruoxia & Cao, Jinde, 2016. "Stability analysis of reaction-diffusion uncertain memristive neural networks with time-varying delays and leakage term," Applied Mathematics and Computation, Elsevier, vol. 278(C), pages 54-69.
    5. Zhang, Chaolong & Deng, Feiqi & Peng, Yunjian & Zhang, Bo, 2015. "Adaptive synchronization of Cohen–Grossberg neural network with mixed time-varying delays and stochastic perturbation," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 792-801.
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    Cited by:

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    3. Aouiti, Chaouki & Ben Gharbia, Imen & Cao, Jinde & Salah M’hamdi, Mohammed & Alsaedi, Ahmed, 2018. "Existence and global exponential stability of pseudo almost periodic solution for neutral delay BAM neural networks with time-varying delay in leakage terms," Chaos, Solitons & Fractals, Elsevier, vol. 107(C), pages 111-127.
    4. Pahnehkolaei, Seyed Mehdi Abedi & Alfi, Alireza & Machado, J.A. Tenreiro, 2019. "Delay independent robust stability analysis of delayed fractional quaternion-valued leaky integrator echo state neural networks with QUAD condition," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 278-293.
    5. Li, Qiaoping & Liu, Sanyang & Chen, Yonggang, 2018. "Combination event-triggered adaptive networked synchronization communication for nonlinear uncertain fractional-order chaotic systems," Applied Mathematics and Computation, Elsevier, vol. 333(C), pages 521-535.
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    7. Xu, Yao & Yu, Jintong & Li, Wenxue & Feng, Jiqiang, 2021. "Global asymptotic stability of fractional-order competitive neural networks with multiple time-varying-delay links," Applied Mathematics and Computation, Elsevier, vol. 389(C).

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