Understanding key terms of dynamical systems theory

Dynamical Systems Theory has been applied to the study of human movement. The strength of the theory is in the tools it provides to mathematically understand change in behavior. However, for anyone reading an article on dynamical systems theory for the first time, they will probably walk away confused.

There are a number of key terms that are used across all disciplines when discussing Dynamical Systems Theory. In this article I describe the meaning of some of these terms.


This refers to the ability of a system to spontaneously organise itself into patterns of coordination (i.e., attractor states).

Attractor states

An attractor state is a stable state of organisation. Think of it as an individual’s coordination tendency. For example, every time we move, our body organizes itself into an attractor state which enables functional movements to occur.


This refers to the ability to switch between multiple attractor states. Multi-stability is important for maintaining functional movements, as sometimes our movements are perturbed and we need to switch to a different coordination pattern. Possessing multiple attractor states is thought to be a characteristic of expert athletes.


This is the region where there are 2 competing tendencies. A good example of a meta-stable region comes from batting in cricket. When the ball is pitched full, batsmen tend to step forward to hit the ball. When the ball is pitched short, batsmen tend to step backwards to hit the ball. However, when the ball is pitched in between, batsman vary between stepping forward and backwards. This represents a meta-stable region as there are 2 competing tendencies (stepping forward and stepping backwards). Practicing within a meta-stable region is thought to be advantageous for improving a player’s ability to transit between 2 attactor states.

Critical fluctuations

This represents the moment when one attractor state switches to another attractor state. This is best illustrated by the bimanual coordination finger moving task. If you move your index fingers left and right in unison with each other, you will be able to do this until the speed reaches a certain threshold. At this threshold, your finger movements will switch from moving in the same direction to the opposite direction.


This refers to the situation when the emergence of an attractor state is heavily influenced by a previous attractor state. Let’s use a table tennis example to illustrate this. Participants were fed table tennis balls via a machine with each ball landing in a different location across the width of table. When the balls landed on the forehand side of the court, participants played a forehand. When the balls landed on the backhand side of the court, participants played a backhand. However, when the ball landed closer to the middle, participants switched between forehands and backhands. And the choice of hitting a forehand or a backhand was influenced by the previous shot (i.e., if a forehand was hit previously, they were more likely to hit a forehand on the next shot). This is an example of hysteresis.

Control parameter

This refers to the variable that causes switching between attractor states. In the table tennis example above, the control parameter was the ball landing location, as this determined whether a forehand or a backhand was played. In the bimanual coordination finger moving task, the control parameter is the speed of finger movements.

Here are some useful references for further reading.


Kelso, J. A. (2009). Coordination dynamics. In Encyclopedia of complexity and systems science (pp. 1537-1565). Springer New York.

Seifert, L., Button, C., & Davids, K. (2013). Key properties of expert movement systems in sport. Sports Medicine43(3), 167-178.

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