Variable-time impulsive control for bipartite synchronization of coupled complex networks with signed graphs

Cluster synchronization of fractional‐order complex networks via variable‐time impulsive control

“…Synchronization is a kind of cooperative behavior in the networks, which refers to the process that multiple subsystems influence each other through information interaction, and all subsystems eventually tend to the same state. According to different performance characteristics, synchronization can be classified as projection synchronization [15], exponential synchronization [16,17], bipartite synchronization [18], cluster synchronization [19][20][21][22][23][24][25], and so on. Among them, cluster synchronization refers to the phenomenon that all dynamic nodes are divided into several clusters in the networks, which belong to the same cluster can reach complete synchronization, while those in different clusters are always desynchronized.…”

“…In recent years, fractional calculus has been introduced into complex dynamic networks, which further improves the design, expression, and control ability of complex dynamic networks. Moreover, complex dynamic networks often exhibit some complex and interesting dynamic behaviors, including consensus [13], flocking [14], and synchronization [15][16][17][18][19][20][21][22][23][24][25].…”

“…At present, many researchers have adopted B-equivalence method to analyze variable-time impulsive system. For instance, [18] has investigated the bipartite synchronization of coupled complex networks with signed graphs via variable-time impulsive control. By using the B-equivalence method, the variable-time impulsive model can be changed the fixed-time impulsive model, and applying mathematical induction, some sufficient conditions for bipartite synchronization have been derived.…”

Dynamics of Symmetrical Discontinuous Hopfield Neural Networks with Poisson Stable Rates, Synaptic Connections and Unpredictable Inputs

“…We provide the initial explanation for the model in the hope that neuroscience specialists will accept and adapt our suggestions further. The symmetry will open up new possibilities for productive application of the methods introduced and developed within the last few years for various types of impulsive systems [20][21][22] and networks [23][24][25]. Another interesting opportunity involves combining methods for discontinuous dynamics with those for synchronization [26,27].…”