Active Brownian particles with energy depots modeling animal mobility

Abstract

In the model of active motion studied here, Brownian particles have the ability to take up energy from the environment to store it in an internal depot and to convert internal energy into kinetic energy. Considering also internal dissipation, we derive a simplified model of active biological motion. For the take-up of energy two different examples are discussed: (i) a spatially homogeneous supply of energy, and (ii) the supply of energy at spatially localized sources (food centers). The motion of the particles is described by a Langevin equation which includes an acceleration term resulting from the conversion of energy. Dependent on the energy sources, we found different forms of periodic motion (limit cycles), i.e. periodic motion between ‘nest’ and ‘food’. An analytic approximation allows the description of the stationary motion and the calculation of critical parameters for the take-up of energy. Finally, we derive an analytic expression for the efficiency ratio of energy conversion, which considers the take-up of energy, compared to (internal and external) dissipation.