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AIMS Mathematics

2021, Volume 6, Issue 10: 10620-10641. doi: 10.3934/math.2021617
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Research article

Synchronizations of fuzzy cellular neural networks with proportional time-delay

  • 1.
    Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi-221005, India
  • 2.
    School of Mathematics, Southeast University, Nanjing 210096, China and Yonsei Frontier Lab, Yonsei University, Seoul 03722, South Korea
  • 3.
    School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha 410114, Hunan, China
  • Received: 01 March 2021 Accepted: 12 July 2021 Published: 23 July 2021

  • MSC : 03E72, 34D20, 43D06, 68T07, 93D40

  • In this article, finite-time and fixed-time synchronizations (FFTS) of fuzzy cellular neural networks (FCNNs) with interaction and proportional delay terms have been investigated. The synchronizations of FCNNs are achieved with the help of p-norm based on the inequalities defined in Lemmas 2.1 and 2.2. The analysis of the method with some useful criteria is also used during the study of FFTS. Under the Lyapunov stability theory, FFTS of fuzzy-based CNNs with interaction and proportional delay terms can be achieved using controllers. Moreover, the upper bound of the settling time of FFTS is obtained. In view of settling points, the theoretical results on the considered neural network models of this article are more general as compared to the fixed time synchronization (FTS). The effectiveness and reliability of the theoretical results are shown through two numerical examples for different particular cases.

    Citation: Ankit Kumar, Subir Das, Vijay K. Yadav, Rajeev, Jinde Cao, Chuangxia Huang. Synchronizations of fuzzy cellular neural networks with proportional time-delay[J]. AIMS Mathematics, 2021, 6(10): 10620-10641. doi: 10.3934/math.2021617

    Related Papers:

  • In this article, finite-time and fixed-time synchronizations (FFTS) of fuzzy cellular neural networks (FCNNs) with interaction and proportional delay terms have been investigated. The synchronizations of FCNNs are achieved with the help of p-norm based on the inequalities defined in Lemmas 2.1 and 2.2. The analysis of the method with some useful criteria is also used during the study of FFTS. Under the Lyapunov stability theory, FFTS of fuzzy-based CNNs with interaction and proportional delay terms can be achieved using controllers. Moreover, the upper bound of the settling time of FFTS is obtained. In view of settling points, the theoretical results on the considered neural network models of this article are more general as compared to the fixed time synchronization (FTS). The effectiveness and reliability of the theoretical results are shown through two numerical examples for different particular cases.


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