On the collective behavior of self-driven individuals

EZEQUIEL V. ALBANO; GABRIEL BAGLIETTO, EZEQUIEL V. ALBANO

San Luis Potosí

Workshop; XII Latin American Workshop on Nonlinear Phenomena (LA; 2011

PLENARIA ALBANOThe study of flocking behavior has attracted interdisciplinary interest due not only to theirfascinating characteristics and their ubiquity in all scales, but also for their complex nature.Modeling of swarming and flocking contributes to the understanding of natural phenomenaand becomes relevant for many practical and technological applications, e.g. collective roboticmotion, design and control of artificial micro swimmers, etc. [1-7]. Within this broad context, theVicsek Model (VM) [2], which considers individuals that try to adopt the direction of movementof their interacting neighbors, under the influence of some noise, e.g. due to the environment, hasgained large popularity becoming an archetypical model for the study of the onset of order uponthe interactive displacement of self-driven individuals. The simple rules of the VM guarantee theobservation of a rather complex and interesting critical behavior: an ordered phase of collectivemotion is found for low enough levels of noise, while a disordered phase is observed at high noise.However, the nature of the phase transition between those phases could be of first-or secondorder,depending on the type of considered noise [4,5,7]. The aim of this paper is to investigatethe structural characteristics of the networks formed among the self-driven individuals duringthe farm-from equilibrium stationary states of the VM. We expect that the proposed studywill shed some light on some poorly understood characteristics of the VM, such as the origin of2ordering, as well as on the nature of the order-disorder observed phase transition, i.e. first- versussecond-order. The collective motion of self-driven individuals leads to the formation of complexspatial-temporal patterns. We performed extensive numerical simulations of the VM showing thatthe structure of the clusters formed upon flocking strongly depends on the nature of the noise.By evaluating relevant network properties such as the average path length, the average degree,the clustering coefficient, etc.. We give evidence on the formation of complex structures with aneffective dimension higher than the dimensionality of the space where the actual displacementstake place. Furthermore, these structures are capable to sustain orientationally ordered stateswhen the displacements are suppressed. We conclude that the structural properties of the clustersformed upon flocking strongly depend on the type of noise affecting the interactions betweenindividuals. The relevance of our findings to the understanding of the onset of long-range orderupon flocking is also discussed.References:1. J. L. Deneubourg and S. Goss, Ethology, Ecology, Evolution 1989, 1: 295.2. T. Vicsek, et al., Phys. Rev. Lett. 1995, 75: 1226-1229.3. G. Theraulaz, et al., Proc. Nat. Acad. Sci. 2002, 99: 645.4. C. Huepe and M. Aldana, Phys. Rev. Lett. 2004, 92: 168701.5. G. Gr´egoire, and H. Chat´e, Phys. Rev. Lett. 2004, 92: 025702.6. T. Feder, Phys Today 2007, 60: 28.7. G. Baglietto and E.V. Albano, Phys. Rev. E 2009, 80: 050103(R), 4pp.