Synchronization scenarios in three-layer networks with a hub

Area of Science:

• Computational neuroscience
• Complex systems dynamics
• Network theory

Background:

• Chimera states, a mixture of coherent and incoherent dynamics, are observed in coupled oscillator networks.
• Neuronal dynamics can be modeled using systems like the FitzHugh-Nagumo oscillators.
• Relay synchronization in multi-layer networks is crucial for information processing.

Purpose of the Study:

• Investigate the role of a central hub in mediating relay synchronization and inducing chimera states.
• Analyze the impact of inter-layer coupling strength and time delay on network dynamics.
• Explore the effects of link dilution on chimera formation and synchronization.

Main Methods:

• Simulations of a three-layer network with a single-node hub and two remote layers of coupled FitzHugh-Nagumo oscillators.
• Systematic variation of inter-layer coupling strength and time delay.
• Analysis of network states including double chimeras and salt-and-pepper states.
• Investigation of link dilution effects.

Main Results:

• The hub is essential for inducing chimera states, especially at low intra-layer coupling.
• Tongue-like regions in parameter space reveal double chimera and salt-and-pepper states.
• Inter-layer coupling strength and time delay significantly influence synchronization and chimera formation.
• Dilution of links to the coherent domain most strongly disrupts chimera states.

Conclusions:

• A single-node hub can act as a critical element for emergent complex dynamics like chimera states in multi-layer neuronal networks.
• Network topology and coupling parameters critically determine the presence and characteristics of synchronized states.
• Targeted removal of connections to coherent regions can effectively destabilize chimera states.