Lévy Walk in Swarm Models Based on Bayesian and Inverse Bayesian Inference

Area of Science:

• Complex systems
• Statistical physics
• Agent-based modeling

Background:

• Swarming behavior in nature often exhibits critical phenomena, resembling phase transitions.
• Critical states in swarming are characterized by patterns like Lévy walks, but a unifying mechanism remains elusive.
• Self-Propelled Particle (SPP) models are widely used to simulate collective motion.

Purpose of the Study:

• To propose a general mechanism explaining the critical properties observed in swarming behavior.
• To investigate the role of Bayesian inference in emergent collective dynamics.
• To compare the predictive power of different SPP models incorporating Bayesian inference.

Main Methods:

• Utilized the Self-Propelled Particle (SPP) model framework.
• Introduced Bayesian inference and inverse Bayesian inference (BIB) for agent decision-making.
• Compared three models: simple SPP, SPP with Bayesian-only inference (BO), and SPP with BIB.

Main Results:

• The BIB model uniquely demonstrated coexisting tornado, splash, and translation behaviors.
• The BIB model successfully reproduced the Lévy walk pattern characteristic of critical states.
• Simple SPP and BO models did not exhibit the full spectrum of critical behaviors observed in the BIB model.

Conclusions:

• Bayesian and inverse Bayesian inference (BIB) provides a viable mechanism for explaining critical phenomena in swarming.
• The proposed BIB approach unifies diverse collective behaviors under a single inferential framework.
• This work offers a novel perspective on the emergence of complex patterns in collective motion.