Basin of attraction determines hysteresis in explosive synchronization.
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.
Department of Physics, East China Normal University, Shanghai 200062, China and Potsdam Institute for Climate Impact Research, P.O. Box 601203, 14412 Potsdam, Germany.
Yong
Y
Zou
Department of Mathematics, Imperial College London, London SW72AZ, United Kingdom and London Mathematical Laboratory, London WC2N 6DF, United Kingdom.
Tiago
T
Pereira
School of Mathematics and Statistics, University of Western Australia, Crawley, Western Australia 6009, Australia.
Michael
M
Small
Department of Physics, East China Normal University, Shanghai 200062, China.
Zonghua
Z
Liu
Potsdam Institute for Climate Impact Research, P.O. Box 601203, 14412 Potsdam, Germany and Institute for Complex Systems and Mathematical Biology, University of Aberdeen, Aberdeen AB243UE, United Kingdom.
Jürgen
J
Kurths
D008962:Models, Theoretical