# Group synchronization of diffusively coupled harmonic oscillators

Liyun Zhao; Jun Liu; Lan Xiang; Jin Zhou

Kybernetika (2016)

- Volume: 52, Issue: 4, page 629-647
- ISSN: 0023-5954

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topZhao, Liyun, et al. "Group synchronization of diffusively coupled harmonic oscillators." Kybernetika 52.4 (2016): 629-647. <http://eudml.org/doc/286827>.

@article{Zhao2016,

abstract = {This paper considers group synchronization issue of diffusively directed coupled harmonic oscillators for two cases with nonidentical and identical agent dynamics. For the case of coupled nonidentical harmonic oscillators with positive coupling, it is demonstrated that distributed group synchronization can always be achieved under two kinds of network structures, i. e., the strongly connected graph and the acyclic partition topology with a directed spanning tree. It is interesting to find that the group synchronization states under acyclic partition are some periodic orbits with the same frequency and are simply related with the initial values of certain group regardless of ones of the other groups. For the case of coupled identical harmonic oscillators with positive and negative coupling, some generic algebraic criteria on group synchronization with both local continuous and instantaneous interaction are established respectively. In particular, an explicit expression of group synchronization states in terms of initial values of the agents can be obtained by the property of acyclic partition topology, and so it is very convenient to yield the desired group synchronization in practical application. Finally, numerical examples illustrate and visualize the effectiveness and feasibility of theoretical results.},

author = {Zhao, Liyun, Liu, Jun, Xiang, Lan, Zhou, Jin},

journal = {Kybernetika},

keywords = {group synchronization; coupled harmonic oscillators; directed topology; acyclic partition; group synchronization; coupled harmonic oscillators; directed topology; acyclic partition},

language = {eng},

number = {4},

pages = {629-647},

publisher = {Institute of Information Theory and Automation AS CR},

title = {Group synchronization of diffusively coupled harmonic oscillators},

url = {http://eudml.org/doc/286827},

volume = {52},

year = {2016},

}

TY - JOUR

AU - Zhao, Liyun

AU - Liu, Jun

AU - Xiang, Lan

AU - Zhou, Jin

TI - Group synchronization of diffusively coupled harmonic oscillators

JO - Kybernetika

PY - 2016

PB - Institute of Information Theory and Automation AS CR

VL - 52

IS - 4

SP - 629

EP - 647

AB - This paper considers group synchronization issue of diffusively directed coupled harmonic oscillators for two cases with nonidentical and identical agent dynamics. For the case of coupled nonidentical harmonic oscillators with positive coupling, it is demonstrated that distributed group synchronization can always be achieved under two kinds of network structures, i. e., the strongly connected graph and the acyclic partition topology with a directed spanning tree. It is interesting to find that the group synchronization states under acyclic partition are some periodic orbits with the same frequency and are simply related with the initial values of certain group regardless of ones of the other groups. For the case of coupled identical harmonic oscillators with positive and negative coupling, some generic algebraic criteria on group synchronization with both local continuous and instantaneous interaction are established respectively. In particular, an explicit expression of group synchronization states in terms of initial values of the agents can be obtained by the property of acyclic partition topology, and so it is very convenient to yield the desired group synchronization in practical application. Finally, numerical examples illustrate and visualize the effectiveness and feasibility of theoretical results.

LA - eng

KW - group synchronization; coupled harmonic oscillators; directed topology; acyclic partition; group synchronization; coupled harmonic oscillators; directed topology; acyclic partition

UR - http://eudml.org/doc/286827

ER -

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