Complex Network Structure of Flocks in the Standard Vicsek Model

Abstract

In flocking models, the collective motion of self-driven individuals leads to the formation of complex spatiotemporal patterns. The Standard Vicsek Model (SVM) considers individuals that tend to adopt the direction of movement of their neighbors under the influence of noise. By performing an extensive complex network characterization of the structure of SVM flocks, we show that flocks are highly clustered, assortative, and non-hierarchical networks with short-tailed degree distributions. Moreover, we also find that the SVM dynamics leads to the formation of complex structures with an effective dimension higher than that of the space where the actual displacements take place. Furthermore, we show that these structures are capable of sustaining mean-field-like orientationally ordered states when the displacements are suppressed, thus suggesting a linkage between the onset of order and the enhanced dimensionality of SVM flocks.

26 pages, 11 figures. To appear in J. Stat. Phys

References in corpus (20)

• Statistical mechanics of complex networks
• Novel type of phase transition in a system of self-driven particles
• Assortative mixing in networks
• Hierarchical organization of modularity in metabolic networks
• Evolution of networks
• Mixing patterns in networks
• Collective motion
• Critical phenomena in complex networks
• Hierarchical Organization in Complex Networks
• Scale-free correlations in bird flocks
• Hierarchical group dynamics in pigeon flocks
• Onset of collective and cohesive motion
• Phase transition in the collective migration of tissue cells: experiment and model
• Are randomly grown graphs really random?
• Phase transitions in systems of self-propelled agents and related network models
• New aspects of the continuous phase transition in the scalar noise model (SNM) of collective motion
• Phase transitions in swarming systems: A recent debate
• Phase transitions induced by complex nonlinear noise in a system of self-propelled agents
• Criticality and the Onset of Ordering in the Standard Vicsek Model
• Nonequilibrium Opinion Spreading on 2D Small-World Networks

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