Synchronization in Dynamical Systems Coupled via Multiple Directed Networks

We study synchronization and consensus in a group of dynamical systems coupled via multiple directed networks. We show that even though the coupling in a single network may not be sufficient to synchronize the systems, combination of multiple networks can contribute to synchronization. We illustrate how the effectiveness of a collection of networks to synchronize the coupled systems depends on the graph topology. In particular, we show that if the graph sum is a directed graph whose reversal contains a spanning directed tree, then the network synchronizes if the coupling is strong enough. This is intuitive as there is a root node that influence every other node via a set of edges where each edge in the set is in one of the networks.

[1]  Xiaoqun Wu,et al.  Master stability functions for complete, intralayer, and interlayer synchronization in multiplex networks of coupled Rössler oscillators. , 2016, Physical review. E.

[2]  Manuela Herman.  Consensus And Synchronization In Complex Networks , 2016 .

[3]  Ivan Bonamassa,et al.  Synchronization in networks with multiple interaction layers , 2016, Science Advances.

[4]  Johan A K Suykens,et al.  Introduction to Focus Issue: synchronization in complex networks. , 2008, Chaos.

[5]  Panos J. Antsaklis,et al.  Learning-Based Event-Triggered Control for Synchronization of Passive Multiagent Systems Under Attack , 2020, IEEE Transactions on Automatic Control.

[6]  Massimiliano de Magistris,et al.  Synchronization in Multiplex Networks of Chua’s Circuits: Theory and Experiments , 2020, IEEE Transactions on Circuits and Systems I: Regular Papers.

[7]  Simone Baldi,et al.  Leaderless Synchronization of Heterogeneous Oscillators by Adaptively Learning the Group Model , 2020, IEEE Transactions on Automatic Control.

[8]  C. Wu.  Perturbation of coupling matrices and its effect on the synchronizability in arrays of coupled chaotic systems , 2003, nlin/0307052.

[9]  Louis Pecora,et al.  Symmetries and cluster synchronization in multilayer networks , 2020, Nature Communications.

[10]  C. Wu.  Synchronization in networks of nonlinear dynamical systems coupled via a directed graph , 2005 .

[11]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[12]  R Sevilla-Escoboza,et al.  Inter-layer synchronization in multiplex networks of identical layers. , 2016, Chaos.

[13]  Mattia Frasca,et al.  Intra-layer synchronization in multiplex networks , 2014, 1407.3283.

[14]  Francesco Sorrentino,et al.  Synchronization of hypernetworks of coupled dynamical systems , 2011, 1105.4674.

[15]  Chai Wah Wu,et al.  Synchronization in arrays of coupled nonlinear systems with delay and nonreciprocal time-varying coupling , 2005, IEEE Transactions on Circuits and Systems II: Express Briefs.

[16]  Chai Wah Wu,et al.  Synchronization in Complex Networks of Nonlinear Dynamical Systems , 2008 .

[17]  Dibakar Ghosh,et al.  Intralayer synchronization in neuronal multiplex network , 2019, The European Physical Journal Special Topics.

[18]  C. Wu.  On bounds of extremal eigenvalues of irreducible and m-reducible matrices , 2005 .

[19]  Jürgen Kurths,et al.  Emergence of synchronization in multiplex networks of mobile Rössler oscillators. , 2018, Physical review. E.

[20]  L. Chua,et al.  Application of Kronecker products to the analysis of systems with uniform linear coupling , 1995 .

[21]  L. Pecora,et al.  Cluster Synchronization in Multilayer Networks: A Fully Analog Experiment with LC Oscillators with Physically Dissimilar Coupling. , 2019, Physical review letters.

[22]  R Sevilla-Escoboza,et al.  Relay synchronization in multiplex networks , 2017, Scientific Reports.

[23]  C. Wu.  Synchronization in coupled arrays of chaotic oscillators with nonreciprocal coupling , 2003 .

[24]  C. W. Wu,et al.  On a matrix inequality and its application to the synchronization in coupled chaotic systems , 2006 .

[25]  Chai Wah Wu,et al.  Synchronization in Coupled Chaotic Circuits and Systems , 2002 .

[26]  Ljupco Kocarev,et al.  Consensus and Synchronization in Complex Networks , 2013 .

[27]  Weihua Zhuang,et al.  Interworking of DSRC and Cellular Network Technologies for V2X Communications: A Survey , 2016, IEEE Transactions on Vehicular Technology.

[28]  L. Chua,et al.  Synchronization in an array of linearly coupled dynamical systems , 1995 .

[29]  Stephen P. Boyd,et al.  Graph Implementations for Nonsmooth Convex Programs , 2008, Recent Advances in Learning and Control.