Exponential Outer Synchronization between Two Uncertain Time-Varying Complex Networks with Nonlinear Coupling

Abstract

This paper studies the problem of exponential outer synchronization between two uncertain nonlinearly coupled complex networks with time delays. In order to synchronize uncertain complex networks, an adaptive control scheme is designed based on the Lyapunov stability theorem. Simultaneously, the unknown system parameters of uncertain complex networks are identified when exponential outer synchronization occurs. Finally, numerical examples are provided to demonstrate the feasibility and effectiveness of the theoretical results.

Recovering node parameters and topologies of uncertain non‐linearly coupled complex networks

“…So far, several outer synchronisation methods have been employed to inferring node parameters and topologies of uncertain complex networks, including complete outer synchronisation [14,15,24,25], generalised outer synchronisation [26,27], exponential outer synchronisation [28], lag synchronisation [29], and anticipatory synchronisation [30,31]. Thereinto, anticipatory synchronisation requires the constructed auxiliary network to achieve outer synchronisation with the future states of the uncertain complex network.…”

Adaptive Finite-Time Mixed Interlayer Synchronization of Two-Layer Complex Networks with Time-Varying Coupling Delay

“…This kind of interlayer synchronization can be also understood as outer synchronization [13] between two coupled networks. In the past decade, it has gained considerable attention-see [11,[13][14][15][16][17][18][19][20] and the references therein. Some control schemes have been proposed to realize all kinds of outer synchronization such as complete outer synchronization [13][14][15][16][17], inverse outer synchronization [18], generalized outer synchronization [19], and finite-time outer synchronization [21].…”

Lag synchronization of uncertain complex dynamical networks with derivative coupling

“…Therefore, it has been designed and applied effectively to explore the synchronization behavior in dynamical network with unknown parameters. In [25], exponential outer synchronization problem between two uncertain nonlinearly coupled networks with constant time delays was discussed. Ji et al examined lag synchronization in drive-response uncertain complex dynamical network having delayed coupling and unknown parameters by adaptive control [8].…”