One node driving synchronisation
Abstract
Abrupt changes of behaviour in complex networks can be triggered by a single node. This work describes the dynamical fundamentals of how the behaviour of one node affects the whole network formed by coupled phaseoscillators with heterogeneous coupling strengths. The synchronisation of phaseoscillators is independent of the distribution of the natural frequencies, weakly depends on the network size, but highly depends on only one key oscillator whose ratio between its natural frequency in a rotating frame and its coupling strength is maximum. This result is based on a novel method to calculate the critical coupling strength with which the phaseoscillators emerge into frequency synchronisation. In addition, we put forward an analytical method to approximately calculate the phaseangles for the synchronous oscillators.
 Publication:

Scientific Reports
 Pub Date:
 December 2015
 DOI:
 10.1038/srep18091
 arXiv:
 arXiv:1509.07389
 Bibcode:
 2015NatSR...518091W
 Keywords:

 Nonlinear Sciences  Adaptation and SelfOrganizing Systems;
 Physics  Physics and Society
 EPrint:
 Chengwei Wang, Celso Grebogi and Murilo S. Baptista. One node driving synchronisation. Sci. Rep. 5 (2015)