Synchronization of singular complex dynamical networks with time-varying delays

Synchronization of continuous-time Markovian jumping singular complex networks with mixed mode-dependent time delays

“…But, by using Theorem 1 in this paper, we can obtain the larger delay bound d m ¼ 3:472. From Table 2, it is clear that Theorem 1 in this paper is less conservative than [4,6].…”

“…For the sake of simplification, we consider a 5-node singular complex neural networks (1) with the following parameters: Remark 8. For the case of constant delay, that is to say _ dðtÞ ¼ 0, by applying the result in [4,6] to this system, when coupled strength c¼ 0.1, the maximum allowable delay bound d m ¼ 2:173. But, by using Theorem 1 in this paper, we can obtain the larger delay bound d m ¼ 3:472.…”

“…It is widely believed that there exist many benefits of having synchronization in many fields, such as secure communication, modelling brain activity and pattern recognition phenomena [1][2][3]. In particular, one of the interesting phenomena in complex networks is the synchronization, which is an important research subject with the rapidly increasing research, and there are a lot of results [4][5][6].…”

“…Koo et al[6]). Given any real matrix M 4 0, any scalars a and b with a o b, and a vector function xðtÞ : ½a; b-R n such that the integrals concerned as well defined, then…”

Impulsive synchronization of Markovian jumping randomly coupled neural networks with partly unknown transition probabilities via multiple integral approach

“…Remark 11: As discussed in Remarks [5] & [10], the criteria existing in (Cao and Li, (2009);Yang and Cao, (2010) ;Yu, Cao and Lu, (2008) ;Yang, Cao and Lu, (2013)) failed with the underlying examples. Koo, Ji and Won, (2010), considered the problem of delay dependent synchronization of singular complex dynamical networks with time-varying delays. Ji, Park, Yoo, Won and Lee, (2010), discussed the synchronization problem for a class of complex dynamical networks in which every identical node is a Lur'e system with time-varying delay.…”