Synchronization-desynchronization transitions in complex networks: an interplay of distributed time delay and...

Area of Science:

• Computational Neuroscience
• Complex Systems Dynamics
• Nonlinear Oscillations

Background:

• Coupled oscillator networks are fundamental models for understanding synchronization phenomena in biological and physical systems.
• The interplay between network topology, node properties (excitatory/inhibitory balance), and signal transmission delays significantly impacts emergent network behavior.
• Stuart-Landau oscillators provide a canonical model for studying the onset and stability of oscillations in various scientific disciplines.

Purpose of the Study:

• To analytically and numerically investigate the stability of synchronous oscillations in a network of coupled Stuart-Landau oscillators under the influence of distributed delays and varying excitatory-inhibitory node ratios.
• To determine the critical conditions under which synchronization transitions from stable to unstable states.
• To explore the role of delay distribution characteristics (width and type) in modulating network stability and inducing resynchronization.

Main Methods:

• Development of a symmetric network model for analytical stability analysis of coupled Stuart-Landau oscillators.
• Analytical investigation of synchronization stability as a function of inhibition ratio and delay distribution parameters.
• Numerical simulations on both symmetric and asymmetrically perturbed network topologies to validate analytical findings.
• Comparison of results using two distinct delay distribution types: uniform and Gamma (Γ) distributions.

Main Results:

• Synchronization stability is compromised beyond a critical inhibition ratio, leading to unstable synchronous oscillations.
• Increasing the width of the delay distribution can counteract the destabilizing effect of high inhibition ratios.
• Multiple resynchronization transitions are observed at relatively high inhibition ratios when delay distributions are sufficiently wide.
• Analytical predictions are confirmed by numerical studies on networks with asymmetric perturbations, demonstrating the robustness of the findings.

Conclusions:

• The balance between excitation and inhibition, coupled with distributed delays, critically governs the stability of synchronous oscillations in complex networks.
• Wider delay distributions offer a mechanism to enhance or restore synchronization in networks with strong inhibitory coupling.
• The findings provide insights into the design principles of stable, synchronized networks and have implications for understanding neural oscillations and other complex systems.