### Abstract

We investigate the avalanche dynamics of the Bak-Tang-Wiesenfeld (BTW) sandpile model on complex networks with general degree distributions. With the threshold height of each node given as its degree in the model, self-organized criticality emerges such that the avalanche size and the duration distribution follow power laws with exponents τ and δ, respectively, Applying the theory of the multiplicative branching process, we find that the exponents τ and δ are given as τ = γ (γ-1) and δ = (γ-1)/(γ-2) for the degree distribution pd(k) ∼ k ^{-γ} with 2 < γ < 3, with a logarithmic correction at γ = 3, while they are 3/2 and 2, respectively, for γ > 3 and when pd(k) follows an exponential-type distribution. The analytic solutions are supported by our numerical simulation results.

Original language | English |
---|---|

Pages (from-to) | 633-637 |

Number of pages | 5 |

Journal | Journal of the Korean Physical Society |

Volume | 44 |

Issue number | 3 I |

Publication status | Published - 2004 Mar 1 |

Externally published | Yes |

### Fingerprint

### Keywords

- Avalanche
- Complex network

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Journal of the Korean Physical Society*,

*44*(3 I), 633-637.

**Branching Process Approach to Avalanche Dynamics on Complex Networks.** / Lee, D. S.; Goh, Kwang-Il; Kahng, B.; Kim, D.

Research output: Contribution to journal › Article

*Journal of the Korean Physical Society*, vol. 44, no. 3 I, pp. 633-637.

}

TY - JOUR

T1 - Branching Process Approach to Avalanche Dynamics on Complex Networks

AU - Lee, D. S.

AU - Goh, Kwang-Il

AU - Kahng, B.

AU - Kim, D.

PY - 2004/3/1

Y1 - 2004/3/1

N2 - We investigate the avalanche dynamics of the Bak-Tang-Wiesenfeld (BTW) sandpile model on complex networks with general degree distributions. With the threshold height of each node given as its degree in the model, self-organized criticality emerges such that the avalanche size and the duration distribution follow power laws with exponents τ and δ, respectively, Applying the theory of the multiplicative branching process, we find that the exponents τ and δ are given as τ = γ (γ-1) and δ = (γ-1)/(γ-2) for the degree distribution pd(k) ∼ k -γ with 2 < γ < 3, with a logarithmic correction at γ = 3, while they are 3/2 and 2, respectively, for γ > 3 and when pd(k) follows an exponential-type distribution. The analytic solutions are supported by our numerical simulation results.

AB - We investigate the avalanche dynamics of the Bak-Tang-Wiesenfeld (BTW) sandpile model on complex networks with general degree distributions. With the threshold height of each node given as its degree in the model, self-organized criticality emerges such that the avalanche size and the duration distribution follow power laws with exponents τ and δ, respectively, Applying the theory of the multiplicative branching process, we find that the exponents τ and δ are given as τ = γ (γ-1) and δ = (γ-1)/(γ-2) for the degree distribution pd(k) ∼ k -γ with 2 < γ < 3, with a logarithmic correction at γ = 3, while they are 3/2 and 2, respectively, for γ > 3 and when pd(k) follows an exponential-type distribution. The analytic solutions are supported by our numerical simulation results.

KW - Avalanche

KW - Complex network

UR - http://www.scopus.com/inward/record.url?scp=1842716624&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=1842716624&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:1842716624

VL - 44

SP - 633

EP - 637

JO - Journal of the Korean Physical Society

JF - Journal of the Korean Physical Society

SN - 0374-4884

IS - 3 I

ER -