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Basin of attraction determines hysteresis in explosive synchronization
Yong Zou1, Tiago Pereira2, Michael Small3
1Department of Physics, East China Normal University, Shanghai 200062, China and Potsdam Institute for Climate Impact Research, P.O. Box 601203, 14412 Potsdam, Germany.
Physical Review Letters
|April 8, 2014
Summary
Spontaneous explosive synchronization occurs in complex networks when node frequencies correlate with node degree. This emergent behavior is driven by changes in the synchronization state
Area of Science:
- Complex networks
- Nonlinear dynamics
- Statistical physics
Background:
- Emergent behavior in complex networks often arises from local interactions.
- Explosive synchronization is a phenomenon characterized by abrupt transitions to a synchronized state.
- Hysteresis is a key feature of explosive synchronization, indicating dependence on system history.
Purpose of the Study:
- To investigate the mechanisms behind spontaneous explosive emergent behavior in heterogeneous networks.
- To understand the origin of hysteretic behavior during transitions to synchronization.
- To explore the influence of microscopic network properties on global network dynamics.
Main Methods:
- Analysis of heterogeneous networks with positively correlated node frequencies and degrees.
- Investigating networks with star graph motifs, including scale-free networks.
- Dynamical analysis to identify the origin of hysteresis.
Main Results:
- Spontaneous explosive emergent behavior is observed when node frequencies correlate positively with node degree.
- Hysteresis at the transition to synchronization is a central feature of this behavior.
- The dynamical origin of hysteresis is identified as a change in the basin of attraction for the synchronization state.
Conclusions:
- Microscopic network parameters like node degree and frequency significantly impact global network properties.
- The findings provide insights into network design and control strategies.
- Understanding these mechanisms is crucial for managing complex systems exhibiting emergent behavior.
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