Adaptive synchronization of weighted complex dynamical networks with coupling time-varying delays

Fuzzy Complex Dynamical Networks and Its Synchronization

“…The Chua's circuit can be easily implemented by simple electronic circuits and hence widely used in complex dynamical networks analysis [3], [7], [11]- [14]. The numerical simulations are done in MATLAB environment.…”

“…Remark 4: Example 5.1, without considering any parametric uncertainties, was discussed in [7], [11], and [14], where it takes approximately seven impulsive time instants to achieve synchronization. In our example, the uncertain complex fuzzy dynamical networks are synchronized within the same time and the α-levels, where 0 ≤ α ≤ 1, of uncertainty in the synchronization errors are also displayed.…”

“…In fact, synchronization is one of the most typical collective behavior and basic motions in nature [5], [6]. Specifically, adaptive rules [7]- [10], impulsive methods [11]- [16], or a combination of them [17], [18] have been used for getting synchronization in networks of coupled chaotic systems.…”

“…However, it should be noted that due to noise and/or uncertainties, the nodes' dynamics do not obey precise state equations, and in most practical situations, only some estimations of them are available [17]. Furthermore, exact prior knowledge about coupling structures and different weightings are usually unavailable [7]. Therefore, a method to completely synchronize the whole network in spite of these uncertainties would be necessary.…”

“…Therefore, a method to completely synchronize the whole network in spite of these uncertainties would be necessary. To deal with unknown network couplings, numerous robust and adaptive methods have been developed [7]- [27], whereas only a few papers addressed the problem of nodes' dynamics uncertainty [10], [14], [15], [26].…”