### Abstract

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

Article number | 62 |

Journal | Frontiers of Physics |

Volume | 5 |

Number of pages | 10 |

ISSN | 2095-0462 |

DOIs | |

Publication status | Published - 2017 |

### Keywords

- Adaptive networks
- Flow networks
- Transport networks
- Heterogeneous network structures
- Transcritical bifurcation
- Tree-like structures

### Cite this

*Frontiers of Physics*,

*5*, [62]. https://doi.org/10.3389/fphy.2017.00062

}

*Frontiers of Physics*, vol. 5, 62. https://doi.org/10.3389/fphy.2017.00062

**Transitions from Trees to Cycles in Adaptive Flow Networks.** / Martens, Erik Andreas; Klemm, Konstantin.

Research output: Contribution to journal › Journal article › Research › peer-review

TY - JOUR

T1 - Transitions from Trees to Cycles in Adaptive Flow Networks

AU - Martens, Erik Andreas

AU - Klemm, Konstantin

PY - 2017

Y1 - 2017

N2 - Transport networks are crucial to the functioning of natural and technological systems. Nature features transport networks that are adaptive over a vast range of parameters, thus providing an impressive level of robustness in supply. Theoretical and experimental studies have found that real-world transport networks exhibit both tree-like motifs and cycles. When the network is subject to load fluctuations, the presence of cyclic motifs may help to reduce flow fluctuations and, thus, render supply in the network more robust. While previous studies considered network topology via optimization principles, here, we take a dynamical systems approach and study a simple model of a flow network with dynamically adapting weights (conductances). We assume a spatially non-uniform distribution of rapidly fluctuating loads in the sinks and investigate what network configurations are dynamically stable. The network converges to a spatially non-uniform stable configuration composed of both cyclic and tree-like structures. Cyclic structures emerge locally in a transcritical bifurcation as the amplitude of the load fluctuations is increased. The resulting adaptive dynamics thus partitions the network into two distinct regions with cyclic and tree-like structures. The location of the boundary between these two regions is determined by the amplitude of the fluctuations. These findings may explain why natural transport networks display cyclic structures in the micro-vascular regions near terminal nodes, but tree-like features in the regions with larger veins.

AB - Transport networks are crucial to the functioning of natural and technological systems. Nature features transport networks that are adaptive over a vast range of parameters, thus providing an impressive level of robustness in supply. Theoretical and experimental studies have found that real-world transport networks exhibit both tree-like motifs and cycles. When the network is subject to load fluctuations, the presence of cyclic motifs may help to reduce flow fluctuations and, thus, render supply in the network more robust. While previous studies considered network topology via optimization principles, here, we take a dynamical systems approach and study a simple model of a flow network with dynamically adapting weights (conductances). We assume a spatially non-uniform distribution of rapidly fluctuating loads in the sinks and investigate what network configurations are dynamically stable. The network converges to a spatially non-uniform stable configuration composed of both cyclic and tree-like structures. Cyclic structures emerge locally in a transcritical bifurcation as the amplitude of the load fluctuations is increased. The resulting adaptive dynamics thus partitions the network into two distinct regions with cyclic and tree-like structures. The location of the boundary between these two regions is determined by the amplitude of the fluctuations. These findings may explain why natural transport networks display cyclic structures in the micro-vascular regions near terminal nodes, but tree-like features in the regions with larger veins.

KW - Adaptive networks

KW - Flow networks

KW - Transport networks

KW - Heterogeneous network structures

KW - Transcritical bifurcation

KW - Tree-like structures

U2 - 10.3389/fphy.2017.00062

DO - 10.3389/fphy.2017.00062

M3 - Journal article

VL - 5

JO - Frontiers of Physics

JF - Frontiers of Physics

SN - 2095-0462

M1 - 62

ER -