### Abstract

We examine the synchronization problem for a group of dynamic agents that communicate via a moving neighborhood network. Each agent is modeled as a random walker in a finite lattice and is equipped with an oscillator. The communication network topology changes randomly and is dictated by the agents' locations in the lattice. Information sharing (talking) is possible only for geographically neighboring agents. This complex system is a time-varying jump nonlinear system. We introduce the concept of 'long-time expected communication network', defined as the ergodic limit of a stochastic time-varying network. We show that if the long-time expected network supports synchronization, then so does the stochastic network when the agents diffuse sufficiently quickly in the lattice.

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

Pages (from-to) | 102-113 |

Number of pages | 12 |

Journal | Physica D: Nonlinear Phenomena |

Volume | 224 |

Issue number | 1-2 |

DOIs | |

State | Published - Dec 2006 |

### Fingerprint

### Keywords

- Fast switching
- Graph
- Random walk
- Stochastic stability
- Synchronization

### ASJC Scopus subject areas

- Applied Mathematics
- Statistical and Nonlinear Physics

### Cite this

*Physica D: Nonlinear Phenomena*,

*224*(1-2), 102-113. https://doi.org/10.1016/j.physd.2006.09.016

**Random talk : Random walk and synchronizability in a moving neighborhood network.** / Porfiri, Maurizio; Stilwell, Daniel J.; Bollt, Erik M.; Skufca, Joseph D.

Research output: Contribution to journal › Article

*Physica D: Nonlinear Phenomena*, vol. 224, no. 1-2, pp. 102-113. https://doi.org/10.1016/j.physd.2006.09.016

}

TY - JOUR

T1 - Random talk

T2 - Random walk and synchronizability in a moving neighborhood network

AU - Porfiri, Maurizio

AU - Stilwell, Daniel J.

AU - Bollt, Erik M.

AU - Skufca, Joseph D.

PY - 2006/12

Y1 - 2006/12

N2 - We examine the synchronization problem for a group of dynamic agents that communicate via a moving neighborhood network. Each agent is modeled as a random walker in a finite lattice and is equipped with an oscillator. The communication network topology changes randomly and is dictated by the agents' locations in the lattice. Information sharing (talking) is possible only for geographically neighboring agents. This complex system is a time-varying jump nonlinear system. We introduce the concept of 'long-time expected communication network', defined as the ergodic limit of a stochastic time-varying network. We show that if the long-time expected network supports synchronization, then so does the stochastic network when the agents diffuse sufficiently quickly in the lattice.

AB - We examine the synchronization problem for a group of dynamic agents that communicate via a moving neighborhood network. Each agent is modeled as a random walker in a finite lattice and is equipped with an oscillator. The communication network topology changes randomly and is dictated by the agents' locations in the lattice. Information sharing (talking) is possible only for geographically neighboring agents. This complex system is a time-varying jump nonlinear system. We introduce the concept of 'long-time expected communication network', defined as the ergodic limit of a stochastic time-varying network. We show that if the long-time expected network supports synchronization, then so does the stochastic network when the agents diffuse sufficiently quickly in the lattice.

KW - Fast switching

KW - Graph

KW - Random walk

KW - Stochastic stability

KW - Synchronization

UR - http://www.scopus.com/inward/record.url?scp=33751011310&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33751011310&partnerID=8YFLogxK

U2 - 10.1016/j.physd.2006.09.016

DO - 10.1016/j.physd.2006.09.016

M3 - Article

VL - 224

SP - 102

EP - 113

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

SN - 0167-2789

IS - 1-2

ER -