Phase ordering in coupled noisy bistable systems on scale-free networks.

Area of Science:

• Complex systems
• Statistical physics
• Network science

Background:

• Bistable elements are fundamental in understanding systems with multiple stable states.
• Noisy systems exhibit complex dynamics influenced by random fluctuations.
• Scale-free networks possess a heterogeneous degree distribution, impacting system behavior.

Purpose of the Study:

• To investigate the phase ordering dynamics in a system of diffusively coupled noisy bistable elements on a scale-free network.
• To analyze the influence of noise intensity on the order-disorder phase transition.
• To elucidate the role of network heterogeneity in the phase ordering process.

Main Methods:

• Simulating a system of diffusively coupled noisy bistable elements.
• Analyzing the system's behavior across varying noise intensities.
• Deriving a nonlinear Fokker-Planck equation under mean-field approximation.
• Utilizing the derived equation to explain observed phase ordering dynamics.

Main Results:

• The system exhibits a clear order-disorder phase transition controlled by noise intensity.
• Phase ordering occurs sequentially based on element degrees, highlighting the network's heterogeneity.
• The nonlinear Fokker-Planck equation accurately describes the network's phase ordering dynamics.

Conclusions:

• Noise intensity is a critical parameter for controlling phase transitions in heterogeneous networks.
• The degree distribution of scale-free networks significantly dictates the order of phase ordering.
• Mean-field approximation provides a valid framework for understanding the dynamics of such complex systems.