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Synchronization in time-varying random networks with vanishing connectivity.
Marco Faggian1,2, Francesco Ginelli1, Fernando Rosas3,4
1SUPA, Physics Department and ICSMB, King's College, University of Aberdeen, AB24 3UE, Aberdeen, UK.
Scientific Reports
|July 17, 2019
Summary
Complex systems can synchronize even with very few connections. Fast rewiring allows partial synchronization in networks with extremely low connectivity, challenging traditional assumptions.
Area of Science:
- Complex systems dynamics
- Network science
- Statistical physics
Background:
- Collective phenomena like synchronization typically require dense network connectivity.
- The role of dynamic network topology in emergence of synchronization is less understood.
Purpose of the Study:
- To investigate synchronization in complex systems with dynamic, rewiring networks and potentially low instantaneous connectivity.
- To determine if synchronization can emerge under conditions of sparse interactions.
Main Methods:
- Modeling a random network of heterogeneous phase oscillators with continuously rearranged links.
- Analyzing system behavior under strong coupling and fast rewiring timescales.
- Developing an approximate analytical argument comparing characteristic timescales in the low connectivity regime.
Main Results:
- Partial synchronization is achieved even in the vanishing connectivity limit with strong coupling and fast rewiring.
- An analytical method accurately predicts the synchronization transition threshold beyond the fast rewiring limit.
- The study demonstrates synchronization is possible despite extremely sparse interactions.
Conclusions:
- Dynamic network topology and fast rewiring can facilitate collective synchronization in complex systems.
- Findings suggest a mechanism for consensus emergence in social networks with sparse communication, relevant to social media dynamics.
- Results offer insights into collective behavior in engineered systems with limited connectivity, such as mobile robots.
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