Dynamical Systems

Previously it was believed humans were controlled by a central mechanism, the brain, which acted similar to a computer and processed all movements (Handford, Davids, Bennett, & Button, 1997). Researchers believed movement patterns were stored in the brain, when an individual re-encountered a similar situation that they had been exposed to previously, the required movement patterns would be recalled to produce the necessary movement for a successful outcome (Handford et al., 1997). Variations that occurred in sporting performances were attributed to noise in the recording systems or variability in the motor control system (Bartlett, Wheat, & Robins, 2007; Davids, Glazier, Araújo, & Bartlett, 2003). More recently, researchers have begun to believe that human cognitive processes are a series of complex interactions between control mechanisms, including the brain, and the environment that interact in order to produce the required movement for the given situation (Chow, Davids, Hristovski, Araújo, & Passos, 2011).

The linear systems approach was proposed by physicists, robotic scientists, engineers and economists who were required to predict behaviours in the respective fields of research. The adoption of a

closed-system approach enabled the researchers to reduce the uncertainty associated with investigating behaviour, therefore increasing the ability to predict actions and outcomes (Glazier & Davids, 2009). However, human movement scientists began to suggest movement was a combination of many individual neurobiological systems interacting to produce a successful movement outcome with respect to different constraints, based on the location of the human body in space and time (Stergiou, Jensen, Bates, Scholten, & Tzetzis, 2001).

Figure 2.5: Newell’s (1986) model of constraints showing the results of the decision making process.

The human decision making process is now seen as a series of complex interactions between the individual and the environment, based on task, environmental and organismic constraints, with variation in movement patterns originating when acquiring new skills (Figure 2.5; Newell, 1986;

Stergiou et al., 2001; Vilar, Araújo, Davids, & Button, 2012). Whilst learning new skills individuals learn the basic movement patterns of a skill and subsequently will experience both success and failure. This experience will allow the individual to learn the boundaries, or degrees of freedom, their body is capable of achieving to perform the skill successfully whilst under

different environmental and task constraints (Chow et al., 2011; Glazier &

Davids, 2009). For example, the basics of passing a football around are constant, although will be dictated by the length of pass required, the positions of both the individuals team mates and opposition players in respect to the individuals starting position as well as the environment such as the type of ball, pitch conditions and weather conditions.

Many differences exist between linear and non-linear systems. In linear systems a change in the behaviour of a system leads to a proportionate change in the outcome, however in non-linear dynamics a small change in the behaviour can lead to a large change in the outcome or performance (Chow et al., 2011). A second difference is; a single input change within a linear system (task, environment or organism) can bring about one effect, yet in non-linear systems one input change can cause many different outcome effects, therefore making judgements or assumptions regarding an individual’s behaviour extremely difficult (Glazier &

Davids, 2009). In non-linear systems it is also possible to train an individual during the learning stage to identify the variability in movements to attain the same desired outcome; this training will in turn be functional to the individual as they learn new ways of overcoming tasks (Chow et al., 2011).

In team sports there is the presence of coupled oscillators, this can be either intra (within team) or inter (between teams). Within a team, players have a direct effect on the options and choices made by the player next to them in the formation they hold, either lateral or longitudinal (Figure 2.6).

These can also be known as dyads, which can be formed or broken depending on the changing situational requirements during the game

(McGarry, Anderson, Wallace, Hughes, & Franks, 2002; Vilar et al., 2012).

For example, in a standard 4-4-2 formation in soccer, the centre backs have an impact on the full backs, centre midfielders and goalkeepers, whilst attackers would generally have impact on the centre midfielders alone, although could also impact on the wide midfielders, depending on the game situation. Inter-couplings exist between teams, for example, in soccer one team’s attackers, alongside the intra-couples with their team’s midfielders, form relationships with the opposition defenders. This is where team formations begin to have an effect on playing styles. For example, if two teams adopt a traditional 4-4-2 players on opposing teams for couplings with the player directly opposite them, however if one team adopts a 4-4-2 and the other players a 3-5-2 or 4-4-1-1, the three defenders will have a more challenging game against 2 attackers compared to having 4 defenders. In addition in a 3-5-2 and a 4-4-1-1, an extra player in midfield occurs, therefore causing more couplings and decisions needing to be made from the team playing 4-4-2.

Both the intra- and inter-couplings are formed by the pursuit of a common goal, the defending team wish to stop the opponents from scoring whilst the attacking team try to break down the defence to score goals (McGarry et al., 2002). Gréhaigne, Bouthier, & David (1997) suggested that soccer players make decisions based on both team’s position, movement and speed, and suggest that the ball holder can cause perturbations or disorder in the defending and attacking rhythm of the game, purely by selecting the appropriate decision. If one team scores a goal, they have been able to sufficiently break the inter-system dyads and have caused the

equilibrium in the match to become unbalanced (Gréhaigne et al., 1997). A similar example can be provided in rugby, where attackers and defenders form dyads, both being attracted to gain ground in front of the position.

During some game actions such as rucks, mauls, scrums or lineouts the dyad is stable and in equilibrium, however if the attacker managers to break the opponents defensive line, a perturbation is caused, breaking the dyads formed and causing the system to become de-stabilised, from this point on the defending team must try to re-gain order and reorganise the defence in order to stop the attacking team from scoring, if the defending team cannot reorganise the defensive formations or cannot complete it rapidly the attacking team will achieve a scoring opportunity (Gréhaigne et al., 1997;

McGarry et al., 2002).

Figure 2.6: An example of dyads formed during a team game (McGarry, Anderson, Wallace, Hughes and Franks, 2002).