### Abstract

Synchronization is often observed in interacting dynamical systems, comprising natural, and technological networks; however, seldom do we have precise knowledge and control over the synchronous trajectory. In this letter, we investigate the possibility of controlling the synchronization of a network by broadcasting from a single reference node. We consider the general case in which broadcasting is not static, but stochastically switches in time. Through an analytical treatment of the Lyapunov exponents of the error dynamics between the network and the reference node, we obtain an explicit dependence of synchronization on the strength of the broadcasting signal, the eigenvalues of the network Laplacian matrix, and the switching probabilities of broadcasting. For coupled chaotic tent maps, we demonstrate that: 1) time averaging fails to predict the onset of controlled synchronization and 2) the success of broadcasting depends on the network topology, where the more heterogeneous the network is, the more difficult it is to control.

Original language | English (US) |
---|---|

Pages (from-to) | 103-108 |

Number of pages | 6 |

Journal | IEEE Control Systems Letters |

Volume | 2 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2018 |

### Fingerprint

### Keywords

- Lyapunov exponents
- Random network
- Scale-free network
- Switching control
- Tent map

### ASJC Scopus subject areas

- Control and Systems Engineering
- Control and Optimization

### Cite this

*IEEE Control Systems Letters*,

*2*(1), 103-108. https://doi.org/10.1109/LCSYS.2017.2756077

**Network synchronization through stochastic broadcasting.** / Jeter, Russell; Porfiri, Maurizio; Belykh, Igor.

Research output: Contribution to journal › Article

*IEEE Control Systems Letters*, vol. 2, no. 1, pp. 103-108. https://doi.org/10.1109/LCSYS.2017.2756077

}

TY - JOUR

T1 - Network synchronization through stochastic broadcasting

AU - Jeter, Russell

AU - Porfiri, Maurizio

AU - Belykh, Igor

PY - 2018/1/1

Y1 - 2018/1/1

N2 - Synchronization is often observed in interacting dynamical systems, comprising natural, and technological networks; however, seldom do we have precise knowledge and control over the synchronous trajectory. In this letter, we investigate the possibility of controlling the synchronization of a network by broadcasting from a single reference node. We consider the general case in which broadcasting is not static, but stochastically switches in time. Through an analytical treatment of the Lyapunov exponents of the error dynamics between the network and the reference node, we obtain an explicit dependence of synchronization on the strength of the broadcasting signal, the eigenvalues of the network Laplacian matrix, and the switching probabilities of broadcasting. For coupled chaotic tent maps, we demonstrate that: 1) time averaging fails to predict the onset of controlled synchronization and 2) the success of broadcasting depends on the network topology, where the more heterogeneous the network is, the more difficult it is to control.

AB - Synchronization is often observed in interacting dynamical systems, comprising natural, and technological networks; however, seldom do we have precise knowledge and control over the synchronous trajectory. In this letter, we investigate the possibility of controlling the synchronization of a network by broadcasting from a single reference node. We consider the general case in which broadcasting is not static, but stochastically switches in time. Through an analytical treatment of the Lyapunov exponents of the error dynamics between the network and the reference node, we obtain an explicit dependence of synchronization on the strength of the broadcasting signal, the eigenvalues of the network Laplacian matrix, and the switching probabilities of broadcasting. For coupled chaotic tent maps, we demonstrate that: 1) time averaging fails to predict the onset of controlled synchronization and 2) the success of broadcasting depends on the network topology, where the more heterogeneous the network is, the more difficult it is to control.

KW - Lyapunov exponents

KW - Random network

KW - Scale-free network

KW - Switching control

KW - Tent map

UR - http://www.scopus.com/inward/record.url?scp=85050793841&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85050793841&partnerID=8YFLogxK

U2 - 10.1109/LCSYS.2017.2756077

DO - 10.1109/LCSYS.2017.2756077

M3 - Article

AN - SCOPUS:85050793841

VL - 2

SP - 103

EP - 108

JO - IEEE Control Systems Letters

JF - IEEE Control Systems Letters

SN - 2475-1456

IS - 1

ER -