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Consistency of heterogeneous synchronization patterns in complex weighted networks.

D Malagarriga¹, A E P Villa², J Garcia-Ojalvo³

¹Departament de Física, Universitat Politècnica de Catalunya. Edifici Gaia, Rambla Sant Nebridi 22, 08222 Terrassa, Spain.

Chaos (Woodbury, N.Y.)

|April 3, 2017

Summary

Complex networks exhibit diverse synchronization patterns, not just homogeneous ones. Heterogeneous coupling and asymmetry in small networks promote varied synchronization, enhancing network consistency.

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Area of Science:

Complex systems
Network science
Dynamical systems

Background:

Synchronization in complex networks is typically assumed to be uniform across all nodes.
Understanding diverse synchronization behaviors is crucial for network analysis.

Purpose of the Study:

To investigate the emergence of diverse synchronization patterns within a single complex network.
To analyze how network properties like coupling heterogeneity and asymmetry influence synchronization diversity and consistency.

Main Methods:

Simulations of interacting oscillators in complex weighted networks.
Analysis of synchronization patterns and their persistence (consistency) under varying initial conditions.
Comparison of synchronization in heterogeneous networks versus regular networks.

Main Results:

Subsets of oscillators within a single network can synchronize in distinct ways.
Increased heterogeneity in coupling weights and asymmetry promote diverse synchronization patterns in small networks.
Complex weighted networks demonstrate richer consistency of coexistent synchronization patterns compared to regular networks.

Conclusions:

Complex networks can exhibit multiple, coexisting synchronization patterns, challenging the assumption of homogeneity.
Network topology, particularly heterogeneity and asymmetry, plays a key role in shaping synchronization dynamics and consistency.
The findings provide insights into the prevalence of specific network topologies observed in experimental data.