The text defines complex systems and points to some main differences between non-living and living systems. It discusses in more detail the differences between linear and nonlinear dynamical systems and point to some necessary concepts important for understanding why nonlinear dynamics is important in explaining sports phenomena. The material is presented in a way suitable for unfamiliar readers to be acquainted with basic terms and meanings from the complex dynamical systems approach to sports. Complex systems may exhibit complex or simple behaviour. An athlete may perform simple arm-curl rhythmic movements but also may be able to perform complex sequences of dribbling actions. On the other hand, simple systems like a single-component nonlinear pendulum may produce simple oscillatory behaviours but also a very complex pattern of chaotic behaviour. Hence, the complexity of behaviour should not be confused with the complexity of the system. Complex systems may behave in a simple fashion because their interacting components, under certain constraints, may form large coalitions of cooperative elements, which reduces the dimensionality of the behaviour. In this way, a complex system attains simple behaviour and may be treated as a simple system on a macroscopic level. We get simplicity from complexity. There are unifying principles that make possible to treat complex systems in a relatively simple fashion. One can also see how the unpredictable behaviours of complex systems arise. The multistability of the system, which is a product of nonlinearity, enables the system to be in more than one state for the same value of parameter. A random event, i.e. a fluctuation, may push the system into a less expected state of organization, perhaps indicative of a lower performance level. Hence, nonlinearity and noise in weakly stable systems might synthesize a behaviour that does not always have to have "a good reason" to emerge. The only way to reduce the probability of such erratic behaviours is to make attractors more stable by changing the control parameter(s) in an adequate direction. But sometimes such weakly stable behaviours are desirable because they may produce novel functional performance behaviours which no one knew existed. In this way, complex systems are also creative, a valuable resource in sport performance.
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