Study of Generalized Synchronization and Anti-synchronization Between Different Dimensional Fractional-Order Chaotic Systems with Uncertainties

• Published in: Differential equations and dynamical systems Vol. 33; no. 3; pp. 849 - 863
• Main Authors: Shukla, Vijay K., Joshi, Mahesh C., Rajchakit, Grienggrai, Chakrabarti, Prasun, Jirawattanapanit, Anuwat, Mishra, Prashant K.
• Format: Journal Article
• Language: English
• Published: New Delhi Springer India 01.07.2025; Springer Nature B.V
• Subjects: Computer Science; Engineering; Mathematics; Mathematics and Statistics; Neural networks; Original Research; Synchronism; Uncertainty; Generalized synchronization; Hopfield neural network; Anti-synchronization; Uncertainties; Fractional-order chaotic system; Cellular neural network
• ISSN: 0971-3514; 0974-6870
• DOI: 10.1007/s12591-023-00653-y

In this article, generalized synchronization between different dimensional chaotic systems has been discussed. Some basic preliminaries and definitions related to generalized synchronization have also been explored. Since during synchronization presence of uncertainties produced huge irregularity so authors studied generalized synchronization between fractional-order chaotic systems with uncertainties. Further, generalized anti-synchronization between fractional-order chaotic systems with uncertainties also investigated. In order to show the effect of uncertainty and fractional-order on generalized synchronization; integer-order generalized synchronization between neural networks (Hopfield and cellular neural networks) without uncertainties also explained. Finally, numerical results agreed with theoretical results.