Sparsity-induced resonance in complex networks

Area of Science:

• Complex Systems
• Network Science
• Nonlinear Dynamics

Background:

• Topological properties significantly influence the collective dynamics of coupled oscillators.
• Understanding resonance phenomena in noisy networks is crucial for various scientific fields.

Purpose of the Study:

• To investigate topology-induced stochastic resonance (SR) and coherence resonance (CR) in coupled noisy networks.
• To explore the role of network sparsity in modulating collective dynamics and resonance phenomena.

Main Methods:

• Analysis of coupled bistable and excitable systems with varying network sparsity.
• Modulation of stochastic switching rates and mean-field coherence based on network structure.
• Application of mean-field theory with a sparsity-dependent effective coupling.

Main Results:

• Demonstrated sparsity-induced SR and CR, with optimal responses occurring at moderate network sparsity.
• Discovered invariant sparsity domains for SR and CR, independent of system size and network type beyond a threshold.
• Mean-field theory successfully predicted sparsity-induced SR.

Conclusions:

• Network sparsity is a key factor in inducing and controlling resonance phenomena in coupled noisy systems.
• The findings offer novel insights into the collective dynamics of biological networks, such as neural connections.
• Provides a potential explanation for astrocyte-mediated pruning of neural connections.