Self-organization of complex networks as a dynamical system

Area of Science:

• Network science
• Complex systems
• Mathematical modeling

Background:

• Real-world networks exhibit dynamic changes.
• Understanding these dynamics is crucial for various fields.
• Previous models often lack the interplay between node states and network structure.

Purpose of the Study:

• To investigate a mathematical model of co-evolving network dynamics.
• To explore the relationship between random walker movement and link weight changes.
• To understand the emergence of network structures and their stability.

Main Methods:

• Developed a mathematical model for random walkers on weighted networks.
• Simulated the co-evolution of walker dynamics and link weights.
• Analyzed the network as a deterministic dynamical system.
• Investigated properties like power-law distributions and system stability.

Main Results:

• Emergence of stationary power-law distributions for resource and link weights under specific conditions.
• Continuous temporal changes in resource quantity at each node.
• Demonstration of multistability, including fixed points, limit cycles, and chaotic states.
• Chaotic system behavior driving microscopic network dynamics without external noise.

Conclusions:

• The intrinsic interplay between node states and network reformation significantly influences real-world network dynamics.
• Co-evolutionary processes are key drivers of network complexity and change.
• The model provides insights into the inherent instability and adaptability of complex networks.