The Open Cybernetics & Systemics Journal

2014, 8 : 455-461
Published online 2014 December 31. DOI: 10.2174/1874110X01408010455
Publisher ID: TOCSJ-8-455

Synchronization in Quotient Network Based on Symmetry

Tao Shaohua , Feng Zhanshen , Luo Jigui and Zhang Zhili
School of Information Engineering, Xuchang University, Henan, 461000, P.R. China.

ABSTRACT

Symmetry is a universal structural property of networks and many real networks have this characteristic. Presently, reducing an original network to a small-size quotient network by means of network symmetry is a promising method for network reduction. This paper studies the synchronization relationship between an original network and its quotient network and concludes that the network and its quotient network reach frequency synchronization simultaneously. We analyze the conclusion in theory and validate it with several simulations on synthetic networks.

Keywords:

Auto-morphism, orbit, original network, quotient network, symmetry network, synchronization.