Affordance-controlled Bifurcations of Action Patterns in Martial Arts

Robert Hristovski, University of St. Cyril and Methodius, Macedonia

Keith Davids, Queensland University of Technology, Australia

Duarte Araújo, Technical University of Lisbon, Portugal

**Abstract: **Effects of participant-target distance and perceived handstriking efficiency on emergent behavior in the martial art of boxing were investigated, revealing affordance-controlled nonlinear dynamical effects (i.e. bifurcations) within the participant – target system. Results established the existence of critical values of scaled distances for emergence of first time excitations and annihilations of a diverse range of boxing actions i.e. on the appearance and dissolution of jabs, hooks and uppercuts. Reasons for the action diversity were twofold: (a) topological discontinuous changes (bifurcations) in the number of possible handstrikes, i.e. motor solutions to the hitting task; (b) fine modification of probabilities of emergence of striking patterns. Exploitation of a ”strikeability” affordance available in scaled distance-to-target information by boxers led to a diversity of emergent actions through a cascade of bifurcations in the task perceptual-motor work space. Data suggested that perceived efficiency (E) of an action changed as a function of scaled distance (D) and was correlated with the probability of occurrence of action patterns (P), exhibiting the following dependence P = P(E(D)). The implication is that probability of occurrence (P) depends on efficiency (E), which in turn depends on scaled distance (D) to the target. Accordingly, scaled distance-dependent perceived efficiency seems a viable candidate for a contextual (control) parameter to describe the nonlinear dynamics of striking actions in boxing.

*Keywords: *action control, bifurcations, affordances, decision-making, motor coordination, nonlinear dynamics, martial arts, action diversity