General hybrid projective complete dislocated synchronization with non-derivative and derivative coupling based on parameter identification in several chaotic and hyperchaotic systems

Abstract

Sun Jun-Wei(孙军伟) a) , Shen Yi(沈 轶) a) † , Zhang Guo-Dong(张国东) a) , Wang Yan-Feng(王延峰) b) , and Cui Guang-Zhao(崔光照) b) a)

Finite-Time Combination-Combination Synchronization for Hyperchaotic Systems

“…. , ) ; that is, the drive systems (8) and (9) are realized as finite-time combinationcombination synchronization with the response systems (10) and (11). …”

“…Our aim is to design a suitable controller, such that the drive systems (8) and (9) are realized as combinationcombination synchronization with the response systems (10) and (11) in finite time. Then, the problem is changed to design a suitable controller, such that the error system (12) achieves the finite-time stability at the origin.…”

“…Furthermore, the drive systems (8) and (9) are realized as combinationcombination synchronization with the response systems (10) and (11) in finite time ≤ , where = 1 + 2 + 3 + 4 .…”

“…The error vector is achieved to zero which implies that systems (8), (9) and (10), (11) have achieved finite-time combination-combination synchronization.…”

“…Since Pecora and Carroll proposed the PC method to synchronize two chaotic systems in 1990 [1,2], the study of synchronization of chaotic systems has been widely investigated due to their potential applications in various fields, for instance, in chemical reactions, biological systems, and secure communication. Over the past decades, a variety of control approaches such as adaptive control [3], linear feedback control [4], active control [5], and backstepping control [6] have been proposed for various types of synchronization, which include complete synchronization [7], projective synchronization [8,9], general synchronization [10], lag synchronization [11], and novel compound synchronization [12].…”