Modeling ants’ walks in patrolling multiple resources using stochastic approximation partial momentum refreshment

In the realm of ant foraging studies, researchers commonly map the movement of ant colonies to Markov Chain Monte Carlo (MCMC) models based on the probability matching strategy, aiming to achieve optimal foraging outcomes. When faced with multiple resources, ants often exhibit remarkable flexibility by patrolling over the foraging area and maximizing resource utilization. However, the regular MCMC models face challenges when resources are multimodally distributed as they struggle to efficiently explore the state space, particularly when modes are distantly separated. Building upon the existing partial momentum refreshment model, we propose a stochastic approximation partial momentum refreshment (SAPMR) model that not only performs equally well as regular MCMC models in bimodal distributions featuring two closely located modes but also overcomes energy barriers associated with multimodal distributions characterized by distantly separated modes. The synthetic data generated using SAPMR exhibits characteristics reminiscent of ants’ behavior such as Lévy-like patterns and maintaining a constant scaling function (≈1) when examining the relationship between the rescaled event speed and the rescaled time.