Synchronizations of fuzzy cellular neural networks with proportional time-delay

• Published in: AIMS mathematics Vol. 6; no. 10; pp. 10620 - 10641
• Main Authors: Kumar, Ankit, Das, Subir, Yadav, Vijay K., Rajeev, Cao, Jinde, Huang, Chuangxia
• Format: Journal Article
• Language: English
• Published: AIMS Press 01.01.2021
• Subjects: finite-time synchronization; fixed-time synchronization; fuzzy cellular neural network; interaction term; proportional delay term
• ISSN: 2473-6988; 2473-6988
• DOI: 10.3934/math.2021617

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.