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 International Conference on Complex Systems (ICCS2007)

Modelling Interpersonal Pattern Dynamics in Team Sports

Pedro Passos
Lusófona University of Humanities and Technologies

Duarte Araújo
Faculty of Human Kinetics/Technical University of Lisbon

Keith Davids
Queensland University of Technology

Ana Diniz
Faculty of Human Kinetics/Technical University of Lisbon

Luis Gouveia
Faculty of Pharmacy/University of Lisbon

Sidónio Serpa
Faculty of Human Kinetics/Technical University of Lisbon

João Milho
Lusófona University of Humanities and Technologies

     Full text: Not available
     Last modified: September 21, 2007

Abstract
In the theory of synergetics, neurobiological behavior emerges from pattern dynamics sustained by behavioral information which guides a system towards a functional attractor. In this presentation we propose a conceptual model that describes emergence of pattern dynamics in the trajectories of an attacker-defender system in a 1 v 1 sub-phase of team sports. Attacker-defender system dynamics in Rugby Union were observed by plotting the angle (x) between a vector connecting defender to attacker and the try line. Collective behavior of the system was defined by changes in x over time, expressed by the equation dx/dt = – dV/dx, where V = V(x) is a potential function. The minima of V correspond to stable states of the system. Empirical evidence suggested that this kind of system has three attractors, namely x = – π/2, x = 0, and x = π/2. Dynamics of attacker-defender dyads in Rugby Union displayed three trajectories characterized as attractors: i) physical contact takes place and the defender stops the attacker; ii) physical contact takes place and the attacker passes the defender; iii) attacker passes the defender without physical contact. Data supported the existence of a potential function of the form V(x) = – k1 x + k2 a x2/2 – b x4/4 + x6/6, where k1 and k2 are two control parameters, a = (π/4)2 * (π/2)2, and b = (π/4)2 + (π/2)2. k1 is the parameter of linear term linked to the attractors – π/2 and π/2, and k2 is the parameter of quadratic term related to attractor 0.







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