Network synchronization, diffusion, and the paradox of heterogeneity

Area of Science:

• Complex networks
• Network synchronization
• Systems biology

Background:

• Complex networks often exhibit heterogeneous degree distributions, impacting network properties.
• Heterogeneity can reduce average distances but paradoxically suppress synchronization in coupled oscillator networks.
• Existing models struggle to explain or resolve this synchronization suppression.

Purpose of the Study:

• To resolve the paradox between network heterogeneity and suppressed synchronization.
• To identify conditions for maximizing network synchronizability.
• To establish a link between network communication processes and synchronization stability.

Main Methods:

• Analysis based on identifying a diffusive process in oscillator communication.
• Relating the diffusive process to the linear stability conditions of synchronized states.
• Investigating weighted and directed coupling strategies.

Main Results:

• Identified a diffusive process crucial for oscillator communication and synchronization stability.
• Demonstrated that maximum synchronizability is achieved with minimum-cost, weighted, and directed couplings.
• Showed that enhanced synchronizability depends solely on mean degree, independent of degree distribution and system size.
• Validated findings using small-world and scale-free network models.

Conclusions:

• Network synchronizability can be maximized by optimizing coupling structure (weighted, directed, minimum cost).
• The mean degree is the sole determinant of enhanced synchronizability, irrespective of network complexity or size.
• Findings offer a novel perspective on controlling synchronization in diverse complex systems.