Resource Concentration and Clustering in Replicator Dynamics with Stochastic Reset Events.

Area of Science:

• Complex Systems
• Theoretical Ecology
• Economic Modeling

Background:

• Replicator dynamics model agent competition for finite resources.
• Stochastic resetting introduces random resets to a small resource value, restarting the process.
• This resetting mechanism significantly alters system dynamics.

Purpose of the Study:

• Investigate the impact of stochastic resetting on replicator dynamics.
• Analyze the resulting resource distribution and statistical behavior.
• Develop analytical approaches to describe the system's evolution.

Main Methods:

• Numerical simulations of replicator dynamics with stochastic resetting.
• Analysis of resource distribution profiles and population size dependence.
• Development of simplified analytical models for entropy and fluctuations.

Main Results:

• Stochastic resetting leads to highly nonuniform resource distributions with significant clustering.
• Observed fluctuations exhibit anomalous dependence on population size, defying mean-field assumptions.
• Simplified analytical models successfully describe entropy evolution and slow fluctuation decrease.

Conclusions:

• Stochastic resetting fundamentally alters resource distribution in competitive systems.
• Non-standard statistical behaviors necessitate advanced analytical methods beyond mean-field.
• The study provides insights into complex system dynamics with resetting mechanisms.