Eur. Phys. J. B 72, 597-606 (2009)
https://doi.org/10.1140/epjb/e2009-00408-8

Dynamics of individuals and swarms with shot noise induced by stochastic food supply

¹ Institute of Physics, Humboldt University Berlin, Newtonstr. 15, 12489 Berlin, Germany
² Mark Kac Complex Systems Research Center, Jagellonian University, Reymonta 4, 30-059 Kraków, Poland
³ Marian Smoluchowski Institute of Physics, Jagellonian University, Reymonta 4, 30-059 Kraków, Poland

Corresponding authors: ^a gudowska@th.if.uj.edu.pl - ^b alsg@physik.hu-berlin.de

Received: 11 May 2009
Published online: 1 December 2009

Abstract

We study the Brownian dynamics of individual particles with energy depot in two dimensions and extend the model to swarms of such particles. We assume that the elements (energy depots) are provided at discrete times with packets of chemical energy which is subsequently converted into acceleration of motion. In contrast to the mechanical white noise which is incorporated in the equations of mechanical motion and has no preferred direction, the energetic noise, as discussed in this study, is directed and it does not reverse the direction of mechanical motion. We characterize the effective noise acting on the particles and show that the stochastic energy supply may be modeled as a shot-noise driven Ornstein-Uhlenbeck process in energy which finally results in fluctuations of the velocity. We study the energy and velocity distributions for different regimes and estimate the crossover time from ballistic to diffusion motion. Further we investigate the dynamics of swarms and find a transition from translational to rotational motion depending on the rate of the shot noise.