A model of reinforced movement leading to spatial learning
Universidad Nacional Autónoma de México (UNAM), Mexico
Memory is considered to play important role for animal home range formation, however few movement models have provided support to this hypothesis mathematically. How experience may lead to repeated visits to some resources sites and cause a restricted space use instead of diffusion is little understood. Here we solve a simple yet non-trivial random walk model which incorporates linear preferential returns to any site visited in the past. When a single resource patch is located in the environment, at a critical rate of memory use the model exhibits a phase transition analogous to a second order phase transition in statistical physics, which separates a diffusive regime from a localized regime. Localization around the resource site emerges spontaneously from the non-Markov movement dynamics and reveals an adaptation to the environment. Our study shows that random walk processes with simple, stereotyped reinforcement rules that require little computation can exhibit spatial learning similarly to foraging animals.