Synchronization of the bidirectionally coupled unified chaotic system via sum of squares method

Abstract

This paper considers the synchronization problem of the bidirectionally coupled unified chaotic system. Many previous works require the assumption that the states of the system are bounded and their range are known. This assumption may not hold for arbitrary controllers, and thus, it is not suitable to make this assumption beforehand. Accordingly, we propose the novel control method for bidirectionally coupled unified chaotic system via sum of squares method without this assumption. Numerical simulations show the validity and advantage of the proposed method.

Identical synchronization of a non-autonomous unified chaotic system with continuous periodic switch

“…The type of coupling defined by (16) and (17) is also called diffusive coupling (Chen et al. 2011; Kim and Chwa 2011; Pikovsky et al. 2001; Shao et al.…”

Composite adaptive fuzzy control for synchronizing generalized Lorenz systems

“…From Eqs. ( 9) and (10), one knows if eð0Þ 2 D a & D, then there exists a finite u ¼ u à in Eq. ( 9) such that lim t!t 1 keðtÞk¼ 0, where D a is a domain of attraction.…”

“…Chaos synchronization is found to be useful in many practical applications such as secure communication, chemical reactions, biological systems, power converters, and information processing, 4 and has been well investigated in recent years. 5 Several model-based control approaches, such as linear feedback control, [6][7][8][9][10] nonlinear feedback control, 9,11,12 and impulsive control, 9 have been applied to synchronize two GLSs.…”