Werner Ebeling, Frank Schweitzer, Benno Tilch:
Active Brownian Particles with Energy Depots
Modelling Animal Mobility
- BioSystems 49 (1999) 17-29
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, (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 convertion 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.
active motion, internal energy depot, animal mobility
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