Search and return model for stochastic path integrators

We extend a recently introduced prototypical stochastic model describing uniformly the search and return of objects looking for new food sources around a given home. The model describes the kinematic motion of the object with constant speed in two dimensions. The angular dynamics is driven by noise and describes a “pursuit” and “escape” behavior of the heading and the position vectors. Pursuit behavior ensures the return to the home and the escaping between the two vectors realizes exploration of space in the vicinity of the given home. Noise is originated by environmental influences and during decision making of the object. We take symmetric α-stable noise since such noise is observed in experiments. We now investigate for the simplest possible case, the consequences of limited knowledge of the position angle of the home. We find that both noise type and noise strength can significantly increase the probability of returning to the home. First, we review shortly main findings of the model presented in the...