### Abstract

The dynamics of large networks is an important and fascinating problem. Key examples are the Internet, social networks, and the human brain. In this paper we consider a model introduced by DeVille and Peskin [6] for a stochastic pulse-coupled neural network. The key feature and novelty in their approach is that they describe the interactions of a neuronal system as a discrete-state stochastic dynamical network. This idealization has two benefits: it captures essential features of neuronal behavior, and it allows the study of spontaneous synchronization, an important phenomenon in neuronal networks that is well-studied but unfortunately far from being well-understood. In synchronous behavior the firing of one neuron leads to the firing of other neurons, which in turn may set off a chain reaction that often involves a substantial proportion of the neurons. In this paper we rigorously analyze their model. In particular, by applying methods and tools that are frequently used in theoretical computer science, we provide a very precise picture of the dynamics and the evolution of the given system. In particular, we obtain insights into the coexistence of synchronous and asynchronous behavior and the conditions that trigger a "spontaneous" transition from one state to another.

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

Title of host publication | Proceedings of the 21st Annual ACM-SIAM Symposium on Discrete Algorithms |

Pages | 949-964 |

Number of pages | 16 |

State | Published - 2010 |

Event | 21st Annual ACM-SIAM Symposium on Discrete Algorithms - Austin, TX, United States Duration: Jan 17 2010 → Jan 19 2010 |

### Other

Other | 21st Annual ACM-SIAM Symposium on Discrete Algorithms |
---|---|

Country | United States |

City | Austin, TX |

Period | 1/17/10 → 1/19/10 |

### Fingerprint

### ASJC Scopus subject areas

- Software
- Mathematics(all)

### Cite this

*Proceedings of the 21st Annual ACM-SIAM Symposium on Discrete Algorithms*(pp. 949-964)

**Synchrony and asynchrony in neural networks.** / Kuhn, Fabian; Panagiotou, Konstantinos; Spencer, Joel; Steger, Angelika.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the 21st Annual ACM-SIAM Symposium on Discrete Algorithms.*pp. 949-964, 21st Annual ACM-SIAM Symposium on Discrete Algorithms, Austin, TX, United States, 1/17/10.

}

TY - GEN

T1 - Synchrony and asynchrony in neural networks

AU - Kuhn, Fabian

AU - Panagiotou, Konstantinos

AU - Spencer, Joel

AU - Steger, Angelika

PY - 2010

Y1 - 2010

N2 - The dynamics of large networks is an important and fascinating problem. Key examples are the Internet, social networks, and the human brain. In this paper we consider a model introduced by DeVille and Peskin [6] for a stochastic pulse-coupled neural network. The key feature and novelty in their approach is that they describe the interactions of a neuronal system as a discrete-state stochastic dynamical network. This idealization has two benefits: it captures essential features of neuronal behavior, and it allows the study of spontaneous synchronization, an important phenomenon in neuronal networks that is well-studied but unfortunately far from being well-understood. In synchronous behavior the firing of one neuron leads to the firing of other neurons, which in turn may set off a chain reaction that often involves a substantial proportion of the neurons. In this paper we rigorously analyze their model. In particular, by applying methods and tools that are frequently used in theoretical computer science, we provide a very precise picture of the dynamics and the evolution of the given system. In particular, we obtain insights into the coexistence of synchronous and asynchronous behavior and the conditions that trigger a "spontaneous" transition from one state to another.

AB - The dynamics of large networks is an important and fascinating problem. Key examples are the Internet, social networks, and the human brain. In this paper we consider a model introduced by DeVille and Peskin [6] for a stochastic pulse-coupled neural network. The key feature and novelty in their approach is that they describe the interactions of a neuronal system as a discrete-state stochastic dynamical network. This idealization has two benefits: it captures essential features of neuronal behavior, and it allows the study of spontaneous synchronization, an important phenomenon in neuronal networks that is well-studied but unfortunately far from being well-understood. In synchronous behavior the firing of one neuron leads to the firing of other neurons, which in turn may set off a chain reaction that often involves a substantial proportion of the neurons. In this paper we rigorously analyze their model. In particular, by applying methods and tools that are frequently used in theoretical computer science, we provide a very precise picture of the dynamics and the evolution of the given system. In particular, we obtain insights into the coexistence of synchronous and asynchronous behavior and the conditions that trigger a "spontaneous" transition from one state to another.

UR - http://www.scopus.com/inward/record.url?scp=77951673448&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77951673448&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:77951673448

SN - 9780898717013

SP - 949

EP - 964

BT - Proceedings of the 21st Annual ACM-SIAM Symposium on Discrete Algorithms

ER -