Adaptive Impulsive Observer for Outer Synchronization of Delayed Complex Dynamical Networks with Output Coupling

Abstract

The synchronization problem of two delayed complex dynamical networks with output coupling is investigated by using impulsive hybrid control schemes, where only scalar signals need to be transmitted from the drive network to the response one. Based on the Lyapunov stability theorem and the impulsive hybrid control method, some sufficient conditions guaranteeing synchronization of such complex networks are established for both the cases of coupling delay and node delay are considered, respectively. Finally, two illustrative examples with numerical simulations are given to show the feasibility and efficiency of theoretical results.

Outer Synchronization of Simple Firefly Discrete Models in Coupled Networks

“…Outer synchronization occurs among coupled complex networks, which means that the corresponding nodes of the coupled networks will achieve synchronization [25][26][27][28][29]. The interaction among communities (or networks) is something that exists in our real world.…”

“…fireflies). From(9) to(28) by choosing = 0, the control inputs 1 = 0; therefore, the five isolated fireflies of the network are unsynchronized assuming different initial conditions.Figures 4 and 5 show the collective behavior of five isolated fireflies oscillators: temporal dynamics of states ( ) and ( ) for = 1, 2, . .…”

Exponential Synchronization of Two Nonlinearly Coupled Complex Networks with Time-Varying Delayed Dynamical Nodes

“…Since chaotic systems defy synchronization, how to design effective controllers for synchronizing coupled chaotic systems becomes an important and challenging problem. Many effective methods including pinning control [11][12][13][14], adaptive control [15][16][17][18][19][20], impulsive control [21][22][23][24][25][26], and intermittent control [27][28][29] have been adopted to design proper controllers. Inner synchronization, that is, the synchronization of all the nodes within a network, has been investigated recently.…”