Self-Organized Coupling Dynamics and Phase Transitions in Bicycle Pelotons

A peloton is a group of cyclists whose individual and collective energy expenditures are reduced when cyclists ride behind others in zones of reduced air pressure; this effect is known in cycling as ‘drafting’. As an aggregate of biological agents (human), a peloton is a complex dynamical system from which patterns of collective behaviour emerge, including phases and transitions between phases, through which pelotons oscillate. Coupling of cyclists’ energy expenditures when drafting is the basic peloton property from which self-organized collective behaviours emerge. Shown here are equations that model coupling behaviours. Environmental constraints are further parameters that affect peloton dynamics. Phases are defined by thresholds of aggregate energy expenditure; shown here are two different, but consistent, conceptual descriptions of these phase transitions. The first is an energetic model that describes phases in terms of individual, bi-coupled and globally-coupled energy output thresholds that define four observable changes in peloton behaviour. A second, economic model incorporates competition and cooperation dynamics: cooperation increases as power outputs and course constraints increase and population diminishes, and where competition and cooperation for resources results in peloton divisions into sub-pelotons whose average fitness levels are more closely homogeneous.