Modular tipping points: How local network structure impacts critical transitions in networked spin systems.
Daniel Reisinger1, Raven Adam1, Fabian Tschofenig1
1Institute of Environmental Systems Sciences, University of Graz, Graz, Styria, Austria.
Plos One
|November 14, 2023
Summary
Network structure significantly impacts critical transitions. High modularity leads to cascading shifts, while low modularity results in unified transitions, highlighting the importance of component roles in networked systems.
Area of Science:
- Complex systems science
- Network theory
- Dynamical systems
Background:
- Critical transitions are abrupt shifts in system states, relevant across ecology, sociology, and physics.
- System network structure critically influences transition dynamics.
- Network modularity is an understudied factor in critical transitions.
Purpose of the Study:
- Investigate the impact of network modularity on critical transition behavior.
- Analyze how altering degree assortativity affects transition dynamics.
- Understand the role of local network structure in system-wide shifts.
Main Methods:
- Simulated critical transitions in networked systems with varying modularity and degree assortativity.
- Controlled manipulation of local network structure via degree assortativity.
- Analysis of transition behavior across diverse degree distributions (e.g., power-law, Poisson).
Main Results:
- High modularity networks exhibit cascading transitions; low modularity networks show unified transitions.
- Networks with heterogeneous node connectivity transition earlier than predicted by average degree.
- Exceptions to earlier transitions occur in low-modularity, high disassortativity networks.
Conclusions:
- Network modularity dictates transition patterns (cascading vs. unified).
- Node connectivity heterogeneity influences transition timing.
- Understanding critical transitions requires analyzing individual components and their network roles.
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