Complex function projective synchronization of general networked chaotic systems by using complex adaptive fuzzy logic

Abstract

This paper is concerned with the problem of complex function projective synchronization for uncertain networked chaotic complex systems. Based on Lyapunov stability, an adaptive control method is proposed for complex modified projective synchronization, which guarantees that the general drive-response networked chaotic complex systems are synchronized up to a complex scaling function matrix. Moreover, a complex fuzzy logic-based observer is designed to compensate for the model uncertainties and the external disturbances that exist in response networks, without prior information about uncertain factors. Numerical simulations are presented to demonstrate the effectiveness of the proposed method.

Fixed-Time Complex Modified Function Projective Lag Synchronization of Chaotic (Hyperchaotic) Complex Systems

“…Recently, some new types of synchronization that utilized complex scaling factors have been introduced to achieve the synchronization of both module and phase, the concept first proposed by Nian et al [14]. Complex complete synchronization (CCoS) [15,16], complex projective synchronization (CPS) [17], combination complex synchronization [18], complex modified projective synchronization (CMPS) [19], and complex function projective synchronization (CFPS) [20,21] are some examples. In these synchronizations, the scaling factors are complex numbers (or functions) that increase the unpredictability and complexity; they have thus significant meaning for enhancing the security of communication [20].…”

“…Observation from [8,20,21] shows that mentioned kinds of synchronizations only are special cases of complex modified function projective synchronization (CMFPS). Furthermore, there might be time delay between drive system and response system from practical point of view [13,20,21]; complex modified function projective lag synchronization (CMFPLS), which is a more general case, is rarely studied or not mentioned up to date.…”

“…In order to obtain such complex synchronization of chaotic (hyperchaotic) complex systems, some control methods such as Lyapunov-based control, feedback control and/or adaptive control [2,5,6,8,[11][12][13][14][15][17][18][19][20], passive control [3], finite-time stability theory-based control [4,9,16], nonlinear observer-based control [7], backstepping-based control [10], and adaptive fuzzy logic control [21] have been proposed. In the mentioned methods, while the ones in [4,9,16] ensure obtaining finite-time synchronization in which the convergence time still depends on both control design parameters 2 Complexity and initial conditions, these remainders guarantee that the synchronization errors might converge to origin asymptotically in the best case.…”