Synchronization in complex dynamical networks coupled with complex chaotic system

Abstract

This paper investigates synchronization in complex dynamical networks with time delay and perturbation. The node of complex dynamical networks is composed of complex chaotic system. A complex feedback controller is designed to realize different component of complex state variable synchronize up to different scaling complex function when complex dynamical networks realize synchronization. The synchronization scaling function is changed from real field to complex field. Synchronization in complex dynamical networks with constant delay and time-varying coupling delay are investigated, respectively. Numerical simulations show the effectiveness of the proposed method.

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.…”

Further improved stability criteria for uncertain T–S fuzzy systems with interval time-varying delay by delay-partitioning approach

“…Since Takagi-Sugeno (T-S) fuzzy model [1] was first introduced, much effort has been made in the stability analysis and control synthesis of such a model during the past three decades, due to the fact that it can combine the flexibility of fuzzy logic theory and fruitful linear system theory into a unified framework to approximate complex nonlinear systems [2][3][4], especially those with incomplete information [1,[5][6][7][8][9].…”