Emergence of coherent motion in aggregates of motile coupled maps

In this paper we study the emergence of coherence in collective motion described by a system of interacting motiles endowed with an inner, adaptative, steering mechanism. By means of a nonlinear parametric coupling, the system elements are able to swing along the route to chaos. Thereby, each motile can display different types of behavior, i.e. from ordered to fully erratic motion, accordingly with its surrounding conditions. The appearance of patterns of collective motion is shown to be related to the emergence of interparticle synchronization and the degree of coherence of motion is quantified by means of a graph representation. The effects related to the density of particles and to interparticle distances are explored. It is shown that the higher degrees of coherence and group cohesion are attained when the system elements display a combination of ordered and chaotic behaviors, which emerges from a collective self-organization process.Comment: 33 pages, 12 figures, accepted for publication at Chaos, Solitons and Fractal

Phase Transitions in Models of Bird Flocking

The aim of the present paper is to elucidate the transition from collective to random behavior exhibited by various mathematical models of bird flocking. In particular, we compare Vicsek’s model [Vicsek et al., Phys. Rev. Lett. 75, 1226–1229 (1995)] with one based on topological considerations. The latter model is found to exhibit a first order phase transition from flocking to decoherence, as the “noise parameter” of the problem is increased, whereas Vicsek’s model gives a second order transition. Refining the topological model in such a way that birds are influenced mostly by the birds in front of them, less by the ones at their sides and not at all by those behind them (because they do not see them), we find a behavior that lies in between the two models. Finally, we propose a novel mechanism for preserving the flock’s cohesion, without imposing artificial boundary conditions or attractive forces