Stochastic resonance on weakly paced scale-free networks

Area of Science:

• Complex Systems
• Nonlinear Dynamics
• Statistical Physics

Background:

• Scale-free networks exhibit inherent degree inhomogeneity.
• Bistable overdamped oscillators are used to model various physical and biological systems.
• Periodic forcing can act as a pacemaker to synchronize network dynamics.

Purpose of the Study:

• To investigate the impact of Gaussian noise and periodic forcing on scale-free oscillator networks.
• To explore the phenomenon of stochastic resonance in weakly paced scale-free networks.
• To determine the crucial role of pacemaker placement and coupling strength in network synchronization.

Main Methods:

• Simulations of a scale-free network of bistable overdamped oscillators.
• Introduction of additive Gaussian noise and weak periodic forcing to a single oscillator (pacemaker).
• Analysis of network response based on pacemaker location (highest vs. lowest degree nodes) and coupling strength.

Main Results:

• An intermediate noise intensity optimally assists the pacemaker in synchronizing the network, indicating stochastic resonance.
• Pacemaker placement is critical due to network inhomogeneity; hub placement leads to a double resonance phenomenon.
• Coupling strength dictates the balance between global synchronization and local correlation, influencing optimal noise levels.

Conclusions:

• Stochastic resonance can occur in weakly paced scale-free networks, with noise playing a constructive role.
• Optimal transmission of weak rhythmic activity across scale-free networks depends on an optimal coupling strength.
• The inhomogeneous structure of scale-free networks significantly influences the dynamics and synchronization of forced oscillators.