Abstract
The problem of projective synchronization of drive-response coupled dynamical network with delayed system nodes and multiple coupling time-varying delays is investigated. Some sufficient conditions are derived to ensure projective synchronization of drive-response coupled network under the impulsive controller by utilizing the stability analysis of the impulsive functional differential equation and comparison theory. Numerical simulations on coupled time delay Lorenz chaotic systems are exploited finally to illustrate the effectiveness of the obtained results.
Highlights
In the past few years, it is found that synchronization is one of the most important and interesting collective behaviors of complex networks and has been extensively investigated in different fields of engineering and sociology [1,2,3,4,5,6,7,8,9,10,11]
When t → ∞, the error system (5) is global exponential asymptotically stable, which implies that the drive-response coupled networks (1) achieve projective synchronization with a scaling factor via impulsive control
We choose impulsive interval Δ = tk+1 − tk = 0.05, and the projective synchronization can be obtained with the given scaling factor α = −2, and the simulation results are as shown in Figures 7, 8, and 9
Summary
In the past few years, it is found that synchronization is one of the most important and interesting collective behaviors of complex networks and has been extensively investigated in different fields of engineering and sociology [1,2,3,4,5,6,7,8,9,10,11]. Sun et al [38] studied the projective synchronization in drive-response dynamical networks of partially linear systems with time-varying coupling delay. Zheng [40] investigated the adaptive-impulsive projective synchronization of drive-response delayed complex dynamical networks with time-varying coupling. Cao et al [32] proposed projective synchronization of a class of delayed chaotic systems via impulsive control, where the drive-response system can be synchronized to within a scaling factor. Analytical results show that drive-response coupled dynamical networks with multiple time delays can realize projective synchronization within a scaling factor. The rest of this paper is organized as follows: in Section 2, the model of drive-response coupled dynamical network with time-varying delays is introduced and some necessary preliminaries are given.
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