A New Lyapunov Function Method to the Fixed-Time Cluster Synchronization of Directed Community Networks

2022 ◽  
Author(s):  
Feilong Zhou ◽  
Xiaobing Nie
Keyword(s):  
Lyapunov Function ◽  
Function Method ◽  
Fixed Time ◽  
Cluster Synchronization ◽  
Community Networks ◽  
Lyapunov Function Method

scholarly journals Hub-Induced Synchronization in Scale-Free Networks with Cluster Structure

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Jianbao Zhang ◽  
Zhongjun Ma ◽  
Jinde Cao
Keyword(s):  
Lyapunov Function ◽  
Function Method ◽  
Cluster Structure ◽  
Sufficient Conditions ◽  
Cluster Synchronization ◽  
Numerical Examples ◽  
Scale Free ◽  
Lyapunov Function Method ◽  
Scale Free Networks ◽  
Theoretical Results

A recent research indicated that the corticocortical connectivity network of the cat possesses cluster structure and that each cluster in the network is scale-free and has a most connected hub. Motivated by that research, we slightly modify the network model and derive sufficient conditions for cluster synchronization of the modified network based on Lyapunov function method. The obtained results indicate that cluster synchronization can be induced by the hubs of the scale-free networks. In our opinion, the concept of hub-induced synchronization provides a better understanding of cluster synchronization in scale-free networks. Numerical examples are provided to demonstrate the effectiveness of the theoretical results.

scholarly journals Pinning Synchronization of Switched Complex Dynamical Networks

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Liming Du ◽  
Feng Qiao ◽  
Fengying Wang
Keyword(s):  
Lyapunov Function ◽  
Complex Networks ◽  
Function Method ◽  
Complex Dynamical Networks ◽  
Switching Topology ◽  
Dynamical Networks ◽  
Switching Law ◽  
Arbitrary Switching ◽  
Lyapunov Function Method ◽  
Networks With Switching Topology

Network topology and node dynamics play a key role in forming synchronization of complex networks. Unfortunately there is no effective synchronization criterion for pinning synchronization of complex dynamical networks with switching topology. In this paper, pinning synchronization of complex dynamical networks with switching topology is studied. Two basic problems are considered: one is pinning synchronization of switched complex networks under arbitrary switching; the other is pinning synchronization of switched complex networks by design of switching when synchronization cannot achieved by using any individual connection topology alone. For the two problems, common Lyapunov function method and single Lyapunov function method are used respectively, some global synchronization criteria are proposed and the designed switching law is given. Finally, simulation results verify the validity of the results.

scholarly journals Independent of delay stabilization using implicit Lyapunov function method

Automatica ◽  
2019 ◽  
Vol 101 ◽  
pp. 103-110
Author(s):  
Konstantin Zimenko ◽  
Denis Efimov ◽  
Andrey Polyakov ◽  
Artem Kremlev
Keyword(s):  
Lyapunov Function ◽  
Function Method ◽  
Lyapunov Function Method

scholarly journals Global Attractivity of a Periodic DelayedN-Species Model of Facultative Mutualism

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Ahmadjan Muhammadhaji ◽  
Zhidong Teng
Keyword(s):  
Lyapunov Function ◽  
Periodic Solutions ◽  
Function Method ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Positive Periodic Solutions ◽  
Facultative Mutualism ◽  
Lyapunov Function Method

Two classes of periodicN-species Lotka-Volterra facultative mutualism systems with distributed delays are discussed. Based on the continuation theorem of the coincidence degree theory developed by Gaines and Mawhin and the Lyapunov function method, some new sufficient conditions on the existence and global attractivity of positive periodic solutions are established.

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