Extension of the Vicsek Model for Collective Motion in Biological Systems

GABRIEL BAGLIETTO; EZEQUIEL V. ALBANO

Cordoba

Congreso; 2º CONGRESO ARGENTINO DE BIOINFORMÁTICA Y BIOLOGÍA COMPUTACIONAL 2011; 2011

Asociación Argentina de Bioinformática y Biología Computacional

Background  Collective  motion  is  an  emergent  phenomenon  found  in  almost  all  scales  in  nature,  ranging  from migrating cells up to mammalian herds. One of the physicist’s approach to this interdisciplinary subject focuses on the study of universal features of minimal models that capture some essential aspects of the problem.  The  Vicsek  Model  (VM)  [1]  is  one  of  the  simplest  possible  models  capable  of  capturing  the main  features  of  collective  motion  in  a  nontrivial  manner.  In  it  point-like  particles  move  at  fixed  speed trying to align locally with their neighbors, but suffering the presence of some noise.  In  previous  works  [2,3]  we  have  studied  the  different  phase  transitions  that  take  place  in  the  system when it is subjected to different kinds of noises. Here we extend the VM in order to consider other types of  perturbations.  It  is  considered  the  possibility  that,  with  a  given  probability  (called  disconnexion probability), each individual, instead of following the rules of the VM, moves in a random direction.  Results  Computational  simulations  of  the  extended  VM  at  zero  noise  are  performed.  By  means  of  finite  size analysis,  study  of  the  behavior  of  the  fourth-order  Binder  cum  ulant,  and  of  the  probability  distribution function  of the  order  parameter,  it  is found  strong  evidence  supporting  the  presence  of  a  new  far-from equilibrium  phase  transition  governed  by  the  disconnexion  probability.  The  bimodal  nature  of  the probability distribution function indicates that this transition is of discontinuous nature.  Conclusions  An  extension  of  the  VM  contemplating  the  possibility  that,  with  a  given  probability,  the  particles  act  at random has been proposed. A new far-from equilibrium phase transition governed by this probability has been found by means of computational simulations. We present evidence of a first order nature of this transition.  References  [1] T. Vicsek, et al., Phys. Rev. Lett. 1995, 75: 1226-1229. [2] G. Baglietto and E.V. Albano, Phys. Rev. E 2008, 78: 021125-021134 [3] G. Baglietto and E.V. Albano, Phys. Rev. E 2009, 80: 050103(R)-05010