### Abstract

This work introduces the phenomenon of Collective Almost Synchronisation (CAS), which describes a universal way of how patterns can appear in complex networks for small coupling strengths. The CAS phenomenon appears due to the existence of an approximately constant local mean field and is characterised by having nodes with trajectories evolving around periodic stable orbits. Common notion based on statistical knowledge would lead one to interpret the appearance of a local constant mean field as a consequence of the fact that the behaviour of each node is not correlated to the behaviours of the others. Contrary to this common notion, we show that various well known weaker forms of synchronisation (almost, time-lag, phase synchronisation, and generalised synchronisation) appear as a result of the onset of an almost constant local mean field. If the memory is formed in a brain by minimising the coupling strength among neurons and maximising the number of possible patterns, then the CAS phenomenon is a plausible explanation for it.

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

Article number | e48118 |

Number of pages | 11 |

Journal | PloS ONE |

Volume | 7 |

Issue number | 11 |

DOIs | |

Publication status | Published - 8 Nov 2012 |

### Fingerprint

### Keywords

- chaos
- systems
- transition
- generalized synchronization
- phase
- behavior

### Cite this

*PloS ONE*,

*7*(11), [e48118]. https://doi.org/10.1371/journal.pone.0048118

**Collective almost synchronisation in complex networks.** / Baptista, Murilo S; Ren, Hai-Peng; Swarts, Johen C M; Carareto, Rodrigo; Nijmeijer, Henk; Grebogi, Celso.

Research output: Contribution to journal › Article

*PloS ONE*, vol. 7, no. 11, e48118. https://doi.org/10.1371/journal.pone.0048118

}

TY - JOUR

T1 - Collective almost synchronisation in complex networks

AU - Baptista, Murilo S

AU - Ren, Hai-Peng

AU - Swarts, Johen C M

AU - Carareto, Rodrigo

AU - Nijmeijer, Henk

AU - Grebogi, Celso

PY - 2012/11/8

Y1 - 2012/11/8

N2 - This work introduces the phenomenon of Collective Almost Synchronisation (CAS), which describes a universal way of how patterns can appear in complex networks for small coupling strengths. The CAS phenomenon appears due to the existence of an approximately constant local mean field and is characterised by having nodes with trajectories evolving around periodic stable orbits. Common notion based on statistical knowledge would lead one to interpret the appearance of a local constant mean field as a consequence of the fact that the behaviour of each node is not correlated to the behaviours of the others. Contrary to this common notion, we show that various well known weaker forms of synchronisation (almost, time-lag, phase synchronisation, and generalised synchronisation) appear as a result of the onset of an almost constant local mean field. If the memory is formed in a brain by minimising the coupling strength among neurons and maximising the number of possible patterns, then the CAS phenomenon is a plausible explanation for it.

AB - This work introduces the phenomenon of Collective Almost Synchronisation (CAS), which describes a universal way of how patterns can appear in complex networks for small coupling strengths. The CAS phenomenon appears due to the existence of an approximately constant local mean field and is characterised by having nodes with trajectories evolving around periodic stable orbits. Common notion based on statistical knowledge would lead one to interpret the appearance of a local constant mean field as a consequence of the fact that the behaviour of each node is not correlated to the behaviours of the others. Contrary to this common notion, we show that various well known weaker forms of synchronisation (almost, time-lag, phase synchronisation, and generalised synchronisation) appear as a result of the onset of an almost constant local mean field. If the memory is formed in a brain by minimising the coupling strength among neurons and maximising the number of possible patterns, then the CAS phenomenon is a plausible explanation for it.

KW - chaos

KW - systems

KW - transition

KW - generalized synchronization

KW - phase

KW - behavior

U2 - 10.1371/journal.pone.0048118

DO - 10.1371/journal.pone.0048118

M3 - Article

C2 - 23144851

VL - 7

JO - PloS ONE

JF - PloS ONE

SN - 1932-6203

IS - 11

M1 - e48118

ER -