Synchronization in node of complex networks consist of complex chaotic system

Abstract

A new synchronization method is investigated for node of complex networks consists of complex chaotic system. When complex networks realize synchronization, different component of complex state variable synchronize up to different scaling complex function by a designed complex feedback controller. This paper change synchronization scaling function from real field to complex field for synchronization in node of complex networks with complex chaotic system. Synchronization in constant delay and time-varying coupling delay complex networks are investigated, respectively. Numerical simulations are provided to show the effectiveness of the proposed method.

Generalized synchronization of different dimensional chaotic dynamical systems in discrete time

“…Therefore, in this case, systems (19) and (20) are generalized synchronized. The error function evolution is shown in Fig.…”

“…Over the past few decades, many synchronization types have been found in interesting chaotic systems [14][15][16][17][18][19][20]. Among all types of synchronization, generalized synchronization (GS) has been extensively considered [21][22][23][24][25].…”

Global asymptotic synchronization of a class of non-linear systems via sampled-data feedback

“…In this section, we will study numerically the synchronization for the original Chua oscillators by applying the theory presented in the previous section. The chaotic synchronization problem has been well-studied under various conditions and some effective approaches have been proposed in recent years (Huang et al, 2012; Huang and Li, 2010; Wang et al, 2010; Wei et al, 2014a,b,c,d,e,f, 2015). As a class of chaotic system, the Chua oscillators intrinsically defy synchronization, because even two identical systems starting from slightly different initial conditions would evolve in time in an unsynchronized manner (the differences in the system states could grow exponentially) (Boccaletti et al, 2002).…”

Adaptive projective synchronization for time-delayed fractional-order neural networks with uncertain parameters and its application in secure communications

“…Since Pecora and Carrol (1990) introduced a method to synchronize two identical chaotic systems with different initial conditions, synchronization has received considerable attention among scientists due to its importance in many applications, such as secure communication, chemical systems, biological systems and human heartbeat regulation. Since then, a variety of synchronization methods have been developed (Shen et al, 2014, 2015; Wang et al, 2013a; Wei et al, 2014c, 2015; Wen et al, 2016a, 2016b), which include adaptive control (Liao and Tsai, 2000), non-linear control (Huang et al, 2004), finite-time synchronization (Wu et al, 2015), sliding mode control (Pourmahmood et al, 2011), neural network-based synchronization (Bagheri et al, 2016) and recurrent hierarchical type-2 fuzzy neural networks-based synchronization (Mohammadzadeh and Ghaemi, 2015). Furthermore, as we know, synchronization exists in various types, such as completer synchronization, lag synchronization, projective synchronization and so on.…”