Adaptive control to synchronize and anti-synchronize two identical time delay Bhalekar-Gejji chaotic systems with unknown parameters

摘要

Based on the Lyapunov-Krasovskii functional theory and using the adaptive control, the work of this paper addresses the globally and asymptotically stable synchronisation and anti-synchronisation between two nearly identical time delay Bhalekar-Gejji chaotic systems in the presence of unknown parameters. Using the drive-response system synchronisation and anti-synchronisation schemes and based on the adaptive control, some algebraic sufficient conditions are derived that guarantee the globally and asymptotically stable synchronisation and anti-synchronisation between two identical time-delay Bhalekar-Gejji chaotic systems. Accordingly, appropriate update laws are designed to identify the fully unknown parameters. It has been shown that the proposed approach has an excellent transient performance in comparison with some noting existing results. Numerical simulations are given to verify and test the effectiveness of the current study.