Decision making in social neurobiological systems modeled as transitions in dynamic pattern formation

Abstract

Extant models of decision making in social neurobiological systems have typically explained task dynamics as characterized by transitions between two attractors. In this paper, we model a three-attractor task exemplified in a team sport context. The model showed that an attacker-defender dyadic system can be described by the angle x between a vector connecting the participants and the try line. This variable was proposed as an order parameter of the system and could be dynamically expressed by integrating a potential function. Empirical evidence has revealed that this kind of system has three stable attractors, with a potential function of the form V(x)=2k 1 x + k 2 ax 2 /22bx 4 /4 + x 6 /6, where k 1 and k 2 are two control parameters. Random fluctuations were also observed in system behavior, modeled as white noise e t , leading to the motion equation dx/dt = 2dV/dx + Q 0.5 e t , where Q is the noise variance. The model successfully mirrored the behavioral dynamics of agents in a social neurobiological system, exemplified by interactions of players in a team sport.

The micro-macro link in understanding sport tactical behaviours: Integrating information and action at different levels of system analysis in sport

“…In the same study, there was a tendency for greater irregularity in the movement of the dyad in successful tackles situations (i.e., providing the basis for a successful move by the defender) and smaller levels of irregularity when tries emerged (i.e., providing the basis for a successful move by the attacker) (see Araújo et al, 2013,, for the complete mathematical model). Building on these observations, Vilar, Araújo,Davids, and Travassos (2012) analyzed the influence on interpersonal coordination tendencies of the relative positioning of competing attacker-defender dyads to the ball and the goal during performance in futsal.…”

Emergence of Contact Injuries in Invasion Team Sports: An Ecological Dynamics Rationale

“…For example, based on the model of Arau´jo et alal. [44], it may be expected that, when a tackle is made by a defender, the contact that may emerge provides a greater risk of injury to one of the sub-system components (i.e. either the dribbling attacker or the defender who is making the tackle).…”

“…The Arau´jo et alal. [44] model may provide a testable framework for predicting levels of injury risk in football dyads since it may describe system symmetry (i.e. 7 The CNS exploitexploits self-organization in a movement system to form temporarily assembled muscle complexes based on specific information picked-uppicked up by the performer.…”

“…For example, Arau´jo et alal. [44] modelled an attacker-defenderattacker-defender dyad system as an order parameter in Rugby.rugby. This order parameter was computed as the angle connecting a vector between the players and the try line.…”

“…Player'sA player's movement pattern may be maintained until a specific phase in which either playersplayer will attempt to de-stabilize the system, causing a symmetry break in the state of the system, where one of the players gains an advantage for achieving the task goal (e.g. passing a defender for scoring or preventing the attacker forfrom doing so)[so) [44].…”