Search and return model for stochastic path integrators

Abstract

1 arXiv:1807.11261v1 [cond-mat.stat-mech] 30 Jul 2018We 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 former manuscript. These are the stationary distance distribution of the noise driven conservative dynamics and the observation of an optimal noise for finding new food sources. Afterwards, we generalize the model by adding a constant shift γ within the interaction rule between the two vectors. The latter might be created by a permanent uncertainty of the correct home position. Non vanishing shifts transform the kinematics of the searcher to a dissipative dynamics. For the latter we discuss the novel deterministic properties and calculate the stationary spatial distribution around the home.

Analysis of aligning active local searchers orbiting around their common home position

“…As solution for the weakly coupled ensemble, we obtain the same stationary marginal density as it was derived for a single independent particle [26,27]. There we have found…”

“…The main ingredient of the kinematics of the searcher is the dynamics of the heading direction standing for the decision making step of the searcher to choose a new direction. In [26,27], we assumedφ…”

Peculiarities of escape kinetics in the presence of athermal noises

“…Divergent moments of Lévy statistics and Lévy motion seem to stay in conflict with energetic and thermodynamics of the stochastic differential equation of the Langevin type 23,44,57,58 . Yet, accumulating evidence shows that Markovian Lévy flights (LFs) with distribution of jumps emerging from the generalized version of the central limit theorem are well suited representations of complex phenomena, to name just a few recent applications of LFs in description of mental searches 61 , analysis of free neutron output in a fusion experiment with a deuteron plasma 56 , investigations of generegulatory networks 62 or examination of self-regulatory motion of insects 63 .…”

Introduction to Focus Issue: Nonlinear science of living systems: From cellular mechanisms to functions

“…Methods of stochastic dynamics are used in modeling active particles and active media, ranging from interactive agents in chemical reactions to socio-dynamics. Noetel et al (2018) describe a simple stochastic kinematic model of search and return, whereby an agent (e.g., an insect or a robot) searches for a target (e.g., a food source) in a noisy environment but is also required to navigate and return to a dock. The study underlines the importance of both the type and the intensity of random perturbations in achieving optimal search performance.…”