Generalized synchronization of complex dynamical networks via impulsive control.
This paper investigates the generalized synchronization (GS) of two typical complex dynamical networks, small-world networks and scale-free networks, in terms of impulsive control strategy. By applying the auxiliary-system approach to networks, we demonstrate theoretically that for any given coupling strength, GS can take place in complex dynamical networks consisting of nonidentical systems. Particularly, for Barabasi-Albert scale-free networks, we look into the relations between GS error and topological parameter m, which denotes the number of edges linking to a new node at each time step, and find out that GS speeds up with increasing m. And for Newman-Watts small-world networks, the time needed to achieve GS decreases as the probability of adding random edges increases. We further reveal how node dynamics affects GS speed on both small-world and scale-free networks. Finally, we analyze how the development of GS depends on impulsive control gains. Some abnormal but interesting phenomena regarding the GS process are also found in simulations.
Chen
Juan
J
School of Mathematics and Statistics, Wuhan University, Hubei 430072, China.
Lu
Jun-An
JA
Wu
Xiaoqun
X
Zheng
Wei Xing
WX
D000465:Algorithms; D003198:Computer Simulation; D005246:Feedback; D017711:Nonlinear Dynamics; D009991:Oscillometry / Q000379:methods*