Active Brownian particles with energy depots modeling animal mobility

In the model of active motion studied here, Brownian particles have the abi lity to take up energy from the environment to store it in an internal depo t and to convert internal energy into kinetic energy. Considering also inte rnal dissipation, we derive a simplified model of active biological motion. For the take-up of energy two different examples are discussed: (i) a spat ially homogeneous supply of energy, and (ii) the supply of energy at spatia lly localized sources (food centers). The motion of the particles is descri bed by a Langevin equation which includes an acceleration term resulting Fr om the conversion of energy. Dependent on the energy sources, we found diff erent 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. (C) 1999 Elsevier Science Ireland Ltd. All rights reserved.