Investigation of the forest-fire model on a small-world network

Area of Science:

• Complex systems
• Network science
• Statistical physics

Background:

• The forest-fire model by Bak et al. is a key model for self-organized criticality.
• Understanding scale-free systems and universality classes is crucial in complex systems research.
• Small-world networks exhibit unique topological properties.

Purpose of the Study:

• To investigate the behavior of the forest-fire model on a square lattice with added long-range interactions.
• To determine if this modified model exhibits self-organized criticality without fine-tuning.
• To explore the impact of increasing long-range interactions on the system's universality class.

Main Methods:

• Simulating the forest-fire model on a square lattice network.
• Introducing long-range interactions to create a small-world network topology.
• Analyzing the cluster size distribution and its exponent.

Main Results:

• The modified forest-fire model generates a scale-free system, characteristic of self-organized criticality.
• No fine-tuning of parameters was required to achieve this scale-free behavior.
• Increasing long-range interactions led to a decrease in the cluster size distribution exponent, signaling a shift in universality class.

Conclusions:

• The forest-fire model on a small-world network naturally produces scale-free behavior.
• The system's universality class changes as the small-world regime is approached.
• This model has potential applications in understanding disease transmission dynamics in populations.