Population dynamics in a random environment

Irene Giardina 1, Jean-Philippe Bouchaud 2, Marc Mézard 3

Journal of Physics A 34 (2001) L245-L252

We investigate the competition between barrier slowing down and proliferation induced superdiffusion in a model of population dynamics in a random force field. Numerical results in $d=1$ suggest that a new intermediate diffusion behaviour appears. We introduce the idea of proliferation assisted barrier crossing and give a Flory like argument to understand qualitatively this non trivial diffusive behaviour. A one loop RG analysis close to the critical dimension d_c=2 confirms that the random force fixed point is unstable and flows towards an uncontrolled strong coupling regime.

  • 1. Service de Physique Théorique (SPhT),
    CNRS : URA2306 – CEA : DSM/SPHT
  • 2. Service de physique de l'état condensé (SPEC),
    CNRS : URA2464 – CEA : DSM/IRAMIS
  • 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
    CNRS : UMR8626 – Université Paris XI - Paris Sud