Cohesive motion in one-dimensional flocking

Abstract

Abstract. A one-dimensional rule-based model for flocking, that combines velocity alignment and long-range centering interactions, is presented and studied. The induced cohesion in the collective motion of the self-propelled agents leads to a unique group behaviour that contrasts with previous studies. Our results show that the largest cluster of particles, in the condensed states, develops a mean velocity slower than the preferred one in the absence of noise. For strong noise, the system also develops a non-vanishing mean velocity, alternating its direction of motion stochastically. This allows us to address the directional switching phenomenon. The effects of different sources of stochasticity on the system are also discussed.

The Effect of Different Communication Mechanisms on the Movement and Structure of Self-Organised Aggregations

“…For model M4, travelling pulses exist for q a − q r < 2, while zigzagging pulses exist for q a − q r > 2. Overall, these results seems to contradict the results in [15], which suggest that a strong attractive interaction can impede the zigzag movement in a 1D individual-based model. However, we note that also for our model, very large attractive interactions (e.g., q a > 10) stop the zigzagging behaviour.…”

“…A second factor, movementfacilitated social interactions (i.e., movement towards or away from conspecifics, or movement to align with conspecifics), has been investigated intensively in the context of pattern formation (see, for ex-ample, [2,8,12,13,17,22,24,25,27,29,31,37,45,46,52], the review in [41] and references therein). Of these mathematical models that investigate the role of social interactions on pattern formation, only a few models are one-dimensional [4,8,13,15,32,40], with the majority being two-or three-dimensional [1,9,14,22,29,30,35,46,50]. Generally, these models consider three social interactions: short-range repulsion, intermediate range alignment/orientation and long-range attraction.…”

“…A generalisation of the model in [40] (which included only alignment) to a more complex model that incorporated attraction, repulsion and alignment, showed that the continuum meanfield limit version of the model does not exhibit zigzagging behaviours [44]. Dossetti [15] also investigated zigzagging behaviour in a 1D individual-based model, and showed numerically that transitions between travelling pulses and zigzagging pulses can be explained by the presence of noise and the differences in the interaction radius of individuals.…”

Flocking in one dimension: effect of update rules

“…Although most of the natural systems of interest are generally two or three dimensional, emergence of collective motion in one dimension has attracted attention in recent times [7,9]. Such one dimensional flocks exhibit the interesting property of direction switching [8,10] and recent theoretical and experimental studies have proven the usefulness of the study of collective motion in one dimension, in particular relevance to the phenomena of directional switching [11,12].…”