Emergent metastable behavior in a resource-constrained network of exclusion processes
Nikhil Bhatia1, Ashish Kumar Pandey2, Arvind Kumar Gupta2
1Institute of Physics, Academia Sinica, Nangang District, Taipei City, Taiwan 115201.
Physical Review. E
|July 24, 2026
Summary
This study models resource-constrained particle flow in a four-lane network, revealing how friction and particle availability create complex phase diagrams and distinct stationary states. Simulations validate analytical findings on phase transitions and metastable behavior.
Area of Science:
- Complex Systems
- Statistical Physics
- Network Science
Background:
- Biological and physical systems exhibit emergent organization through interacting subsystems and resource competition.
- Network models are crucial for understanding particle flow dynamics under constraints.
Purpose of the Study:
- To analyze the stationary-state behavior of a four-lane branching-merging network under resource constraints.
- To investigate the impact of friction and particle filling factor on system dynamics and phase transitions.
Main Methods:
- Analytical derivation of stationary-state attributes using mean-field approximations.
- Stochastic Monte Carlo simulations employing the Gillespie algorithm for validation.
- Construction of phase diagrams in parameter space for different friction regimes.
Main Results:
- Analytical expressions for lane densities, flux, stationary phases, and phase boundaries were obtained.
- Low friction regime shows up to five stationary phases, including a metastable region dependent on initial conditions.
- High friction regime exhibits up to 11 stationary phases, with richer phase diagrams and no metastable behavior.
- Phase diagram complexity and number of phases show non-monotonic behavior with increasing particle input.
Conclusions:
- The study provides a comprehensive understanding of phase transitions in resource-constrained networks.
- Friction and particle availability are key determinants of system complexity and emergent behavior.
- Findings offer insights into phenomena ranging from traffic flow to biological transport.
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