Basin of Attraction Determines Hysteresis in Explosive Synchronization

Yong Zou*, Tiago Pereira, Michael Small, Zonghua Liu, Juergen Kurths

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

111 Citations (Scopus)


Spontaneous explosive emergent behavior takes place in heterogeneous networks when the frequencies of the nodes are positively correlated to the node degree. A central feature of such explosive transitions is a hysteretic behavior at the transition to synchronization. We unravel the underlying mechanisms and show that the dynamical origin of the hysteresis is a change of basin of attraction of the synchronization state. Our findings hold for heterogeneous networks with star graph motifs such as scale-free networks, and hence, reveal how microscopic network parameters such as node degree and frequency affect the global network properties and can be used for network design and control.

Original languageEnglish
Article number114102
Number of pages5
JournalPhysical Review Letters
Issue number11
Publication statusPublished - 18 Mar 2014


  • complex networks
  • scale-free


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