scholarly journals Synchronizability of Multi-Layer Dual-Center Coupled Star Networks

2021 ◽  
Vol 9 ◽  
Author(s):  
Jian Zhu ◽  
Da Huang ◽  
Zhiyong Yu ◽  
Ping Pei
Keyword(s):  
Complex Networks ◽  
Numerical Simulations ◽  
Network Structure ◽  
Single Layer ◽  
Ring Networks ◽  
Laplacian Spectrum ◽  
Single Center ◽  
Stability Function ◽  
Star Networks ◽  
Theoretical Results

In the research on complex networks, synchronizability is a significant measurement of network nature. Several research studies center around the synchronizability of single-layer complex networks and few studies on the synchronizability of multi-layer networks. Firstly, this paper calculates the Laplacian spectrum of multi-layer dual-center coupled star networks and multi-layer dual-center coupled star–ring networks according to the master stability function (MSF) and obtains important indicators reflecting the synchronizability of the above two network structures. Secondly, it discusses the relationships among synchronizability and various parameters, and numerical simulations are given to illustrate the effectiveness of the theoretical results. Finally, it is found that the two sorts of networks studied in this paper are of the same synchronizability, and compared with that of a single-center network structure, the synchronizability of two dual-center structures is relatively weaker.

scholarly journals Adaptive Exponential Synchronization of Coupled Complex Networks on General Graphs

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Song Liu ◽  
Xianfeng Zhou ◽  
Wei Jiang ◽  
Yizheng Fan
Keyword(s):  
Complex Networks ◽  
Numerical Simulations ◽  
Coupling Strength ◽  
Weighted Graph ◽  
Complex Dynamical Networks ◽  
Adaptive Synchronization ◽  
Exponential Rate ◽  
General Graphs ◽  
Theoretical Results ◽  
Variable Coupling

We investigate the synchronization in complex dynamical networks, where the coupling configuration corresponds to a weighted graph. An adaptive synchronization method on general coupling configuration graphs is given. The networks may synchronize at an arbitrarily given exponential rate by enhancing the updated law of the variable coupling strength and achieve synchronization more quickly by adding edges to original graphs. Finally, numerical simulations are provided to illustrate the effectiveness of our theoretical results.

scholarly journals Synchronization in Networks With Heterogeneous Adaptation Rules and Applications to Distance-Dependent Synaptic Plasticity

2021 ◽  
Vol 7 ◽  
Author(s):  
Rico Berner ◽  
Serhiy Yanchuk
Keyword(s):  
Synaptic Plasticity ◽  
Long Range ◽  
Network Structure ◽  
Function Approach ◽  
Adaptive Networks ◽  
Ring Networks ◽  
Phase Oscillators ◽  
Stability Function ◽  
Master Stability Function ◽  
Adaptation Rules

This work introduces a methodology for studying synchronization in adaptive networks with heterogeneous plasticity (adaptation) rules. As a paradigmatic model, we consider a network of adaptively coupled phase oscillators with distance-dependent adaptations. For this system, we extend the master stability function approach to adaptive networks with heterogeneous adaptation. Our method allows for separating the contributions of network structure, local node dynamics, and heterogeneous adaptation in determining synchronization. Utilizing our proposed methodology, we explain mechanisms leading to synchronization or desynchronization by enhanced long-range connections in nonlocally coupled ring networks and networks with Gaussian distance-dependent coupling weights equipped with a biologically motivated plasticity rule.

Further Analysis of Global Synchronisation for Networks of Identical Cells with Delayed Coupling

2015 ◽  
Vol 5 (3) ◽  
pp. 238-255 ◽  
Author(s):  
Chun-Hsien Li ◽  
Ren-Chuen Chen
Keyword(s):  
Dynamical Systems ◽  
Linear System ◽  
Complex Networks ◽  
Numerical Simulations ◽  
Time Delays ◽  
Large Scale ◽  
Collective Motions ◽  
Delay Dependent ◽  
Homogeneous Linear ◽  
Theoretical Results

AbstractSynchronisation is one of the most interesting collective motions observed in large-scale complex networks of interacting dynamical systems. We consider global synchronisation for networks of nonlinearly coupled identical cells with time delays, using an approach where the synchronisation problem is converted to solving an homogeneous linear system. This approach is extended to fit networks under more general coupling topologies, and we derive four delay-dependent and delay-independent criteria that ensure the coupled dynamical network is globally synchronised. Some examples show that the four criteria are not mutually inclusive, and numerical simulations also demonstrate our theoretical results.

Cluster Mixed Synchronization of Complex Networks with Disturbance

2015 ◽  
Vol 719-720 ◽  
pp. 448-451
Author(s):  
Li Jie Zeng
Keyword(s):  
Community Structure ◽  
Complex Networks ◽  
Numerical Simulations ◽  
Network Model ◽  
Complex Dynamical Networks ◽  
Time Varying ◽  
Dynamical Networks ◽  
Bounded Disturbances ◽  
Synchronization Scheme ◽  
Theoretical Results

In this paper, we investigate the cluster mixed synchronization scheme in time-varying delays coupled complex dynamical networks with disturbance. Basing on the community structure of the networks, some sufficient criteria are derived to ensure cluster mixed synchronization of the network model. Particularly, unknown bounded disturbances can be conquered by the proposed control. The numerical simulations are performed to verify the effectiveness of the theoretical results

scholarly journals Condensation of Synchronous Orbits on Complex Networks

2021 ◽  
Author(s):  
Ruiwu Niu ◽  
Xiaoqun Wu ◽  
Jianwen Feng ◽  
Gui-jun Pan ◽  
Jun-an Lu ◽  
...  
Keyword(s):  
Statistical Mechanics ◽  
Complex Networks ◽  
Numerical Simulations ◽  
Phase Synchronization ◽  
Single Layer ◽  
The Other ◽  
Frequency Synchronization ◽  
Synchronization Process ◽  
Mechanics Analysis ◽  
Kuramoto Oscillators

Abstract In this paper we study frequency synchronization of Kuramoto oscillators. We find a typical phenomenon of condensed synchronous orbits on single-layer or duplex networks through statistical mechanics analysis and numerical simulations, where the distribution of synchronous orbits is in a bell-shaped form. Further, we investigate phase synchronization on single-layer and duplex networks with different distributions of inherent frequencies. We find that normally distributed inherent frequencies with low variances are more beneficial for phase synchronization, and separately distributed inherent frequencies can slow down the synchronization process. In the end, we investigate the influence of one layer's inherent frequencies on the other layer's phase synchronization through inter-layer couplings. Interestingly, we find that one layer's inherent frequencies with a highly condensed distribution can greatly improve phase synchronization on the other layer. The results shed new lights to our understanding of the nature of synchronization on single-layer as well as multilayer complex networks of coupled Kuramoto oscillators.

scholarly journals Cluster Synchronization of Nonlinearly Coupled Complex Networks via Pinning Control

2011 ◽  
Vol 2011 ◽  
pp. 1-23 ◽  
Author(s):  
Jianwen Feng ◽  
Jingyi Wang ◽  
Chen Xu ◽  
Francis Austin
Keyword(s):  
Complex Networks ◽  
Numerical Simulations ◽  
Coupling Strength ◽  
Topological Structure ◽  
Sufficient Conditions ◽  
Pinning Control ◽  
Cluster Synchronization ◽  
General Complex ◽  
Coupling Strengths ◽  
Theoretical Results

We consider a method for driving general complex networks into prescribed cluster synchronization patterns by using pinning control. The coupling between the vertices of the network is nonlinear, and sufficient conditions are derived analytically for the attainment of cluster synchronization. We also propose an effective way of adapting the coupling strengths of complex networks. In addition, the critical combination of the control strength, the number of pinned nodes and coupling strength in each cluster are given by detailed analysis cluster synchronization of a special topological structure complex network. Our theoretical results are illustrated by numerical simulations.

scholarly journals Synchronizability of Multilayer Star and Star-Ring Networks

2020 ◽  
Vol 2020 ◽  
pp. 1-20 ◽  
Author(s):  
Yang Deng ◽  
Zhen Jia ◽  
Feimei Yang
Keyword(s):  
Structural Parameters ◽  
Interlayer Coupling ◽  
Ring Networks ◽  
Stability Function ◽  
Eigenvalue Spectrum ◽  
Number Of Layers ◽  
Analytic Expressions ◽  
Coupling Strengths ◽  
The Relationship ◽  
Theoretical Results

Synchronization of multilayer complex networks is one of the important frontier issues in network science. In this paper, we strictly derived the analytic expressions of the eigenvalue spectrum of multilayer star and star-ring networks and analyzed the synchronizability of these two networks by using the master stability function (MSF) theory. In particular, we investigated the synchronizability of the networks under different interlayer coupling strength, and the relationship between the synchronizability and structural parameters of the networks (i.e., the number of nodes, intralayer and interlayer coupling strengths, and the number of layers) is discussed. Finally, numerical simulations demonstrated the validity of the theoretical results.

scholarly journals Cluster Anti-Synchronization of Complex Networks with Nonidentical Dynamical Nodes

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Shuguo Wang ◽  
Chunyuan He ◽  
Hongxing Yao
Keyword(s):  
Community Structure ◽  
Complex Networks ◽  
Numerical Simulations ◽  
Network Model ◽  
Complex Dynamical Networks ◽  
Time Varying ◽  
Dynamical Networks ◽  
Nonidentical Nodes ◽  
Theoretical Results

This paper investigates a new cluster antisynchronization scheme in the time-varying delays coupled complex dynamical networks with nonidentical nodes. Based on the community structure of the networks, the controllers are designed differently between the nodes in one community that have direct connections to the nodes in other communities and the nodes without direct connections with the nodes in other communities strategy; some sufficient criteria are derived to ensure cluster anti-synchronization of the network model. Particularly, the weight configuration matrix is not assumed to be irreducible. The numerical simulations are performed to verify the effectiveness of the theoretical results.

scholarly journals Cluster Synchronization of Time-Varying Delays Coupled Complex Networks with Nonidentical Dynamical Nodes

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Shuguo Wang ◽  
Hongxing Yao ◽  
Mingping Sun
Keyword(s):  
Community Structure ◽  
Complex Networks ◽  
Numerical Simulations ◽  
Network Model ◽  
Complex Dynamical Networks ◽  
Cluster Synchronization ◽  
Time Varying ◽  
Dynamical Networks ◽  
Synchronization Scheme ◽  
Theoretical Results

This paper investigates a new cluster synchronization scheme in the nonlinear coupled complex dynamical networks with nonidentical nodes. The controllers are designed based on the community structure of the networks; some sufficient criteria are derived to ensure cluster synchronization of the network model. Particularly, the weight configuration matrix is not assumed to be symmetric, irreducible. The numerical simulations are performed to verify the effectiveness of the theoretical results.

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