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Griffiths phases in infinite-dimensional, non-hierarchical modular networks.
Wesley Cota1, Géza Ódor2, Silvio C Ferreira3,4
1Departamento de Física, Universidade Federal de Viçosa, 36570-000, Viçosa, Minas Gerais, Brazil. wesley.cota@ufv.br.
Scientific Reports
|June 16, 2018
Summary
This study shows that complex systems with modular structures, not necessarily hierarchical, can exhibit critical behavior. Loosely coupled modules in these networks slow down extinction, leading to Griffiths phases (GPs) without fine-tuning.
Area of Science:
- Complex systems
- Network science
- Statistical physics
Background:
- Griffiths phases (GPs) explain critical behavior in complex systems via network heterogeneities.
- GPs were previously thought to require hierarchical modular network structures.
- Activity spreading models are used to study dynamical behavior on networks.
Purpose of the Study:
- To investigate the dynamical behavior of activity spreading on non-hierarchically organized modular networks.
- To determine if Griffiths phases can emerge in systems lacking hierarchical modularity.
- To relax constraints on network structure for observing critical phenomena.
Main Methods:
- Simulated an activity spreading model on heterogeneous random networks.
- Focused on networks with highly modular but non-hierarchical organization.
- Analyzed dynamical exponents and avalanche size distributions.
Main Results:
- Loosely coupled modules acted as rare regions, delaying activation extinction.
- Extended control parameter regions with continuously changing dynamical exponents were observed.
- Avalanche size distributions showed robust power-law tails, characteristic of critical phenomena.
- Findings were preserved after finite size analyses.
Conclusions:
- Griffiths phases can occur in modular systems without hierarchical organization.
- This research broadens the applicability of the Griffiths phase framework to diverse modular network structures.
- The study provides a mechanism to rationalize criticality in non-hierarchical modular systems.
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