Adaptive pinning synchronization in fractional-order uncertain complex dynamical networks with delay

Synchronization of Time Delayed Fractional Order Chaotic Financial System

“…Lemma 4 (see [23]). Suppose ( ) ∈ 1 is a continuously differentiable and nonnegative function, satisfying…”

Pinning and adaptive synchronization of fractional-order complex dynamical networks with and without time-varying delay

“…But very few authors have discussed adjusting the feedback gains and coupling strength. In [30], by the comparison principle, the synchronization of fractional-order complex dynamical networks with delay is realized via adaptive control. In this paper, we mainly use Razumikhin-type stability theory and the matrix inequality technique to realize synchronization.…”

“…But in the real world, it is too costly and impractical if all of the nodes in the network are controlled. However, many existing works show that we can synchronize the whole network by using pinning control [25][26][27][28][29][30]. Li et al [25] provided several low-dimensional criteria for the synchronization of fractional-order complex dynamical networks with periodically intermittent pinning control.…”

Exponential H∞ synchronization of non-fragile sampled-data controlled complex dynamical networks with random coupling and time varying delay

“…In real world applications, time delays are inevitable in most physical systems (Li, Dong, Han, Hou, & Li, 2017;Lu & Chen, 2004;Park, Kwon, Park, Lee, & Cha, 2012;Yang, Dong, Wang, Ren, & Alsaadi, 2016), therefore it is important to be considered in the investigation of synchronization of CDNs under the exponential H ∞ approach. The existence of time delays which might occur as a result of, limited information channels and large-scale interconnected complex networks could lead to undesired oscillation, instability and poor performance of the CDNs (Lakshmanan et al, 2014;Liang, Wu, & Chen, 2016;Zeng et al, 2015).…”