The Importance of Dynamic Systems | by Teun Thomassen

The importance of dynamical systems theory lies in its ability to provide a valuable framework for understanding the complexity of systems in a world where change is the only constant. This theory not only enhances theoretical understanding but also enables practical applications in various scientific and applied contexts, including physics, biology, psychology, and economics. Moreover, it plays a crucial role in processes related to the organization and learning of movement coordination. Exploring the concepts of dynamical systems and complex systems is essential before delving into why this theory is significant for sports and rehabilitation practices. 

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Dynamical systems and complex systems

These two terms are closely related but not entirely synonymous concepts. It falls outside the scope of this article to fully delve into this, but here are some characteristics. Dynamical systems theory can be seen as a subset of complex systems theory, focusing specifically on the dynamics of systems that change over time. It provides tools and concepts for analyzing the temporal behavior of (simple or) complex systems and understanding how their dynamics emerge from the interactions between components. 

Complex systems theory, on the other hand, offers a broader framework for studying the properties and behaviors of systems with multiple interacting components, encompassing both dynamic and static aspects. In practice, dynamical systems theory is often applied within the context of complex systems to analyze the temporal evolution of system behavior and understand how it emerges from the interactions between its constituent parts. For convenience, in this article I will use the term “complex dynamical system”, the moving body in the (often chaotic) sports context. 

What is the dynamical systems theory?

Dynamical systems theory is an interdisciplinary theoretical framework used to understand and model the complex and often nonlinear dynamics of systems. As previously mentioned, this theory is applied across various fields. In Jane Clark's article, four essential concepts of the theory are described:

• Constraints: This concept suggests that movement arises through given limits or set boundaries surrounding the system. These constraints were further categorized by Karl Newell into task, individual, and environmental constraints.

• Self-Organization: The organization of movement patterns emerges spontaneously from the constraints and is not orchestrated by a "little man in the brain" issuing commands.

• Patterns: Regular, repeating structures or behaviors that result from the interaction of elements within the system. Patterns exhibit characteristics such as convergence to stability and often have seemingly random and unpredictable dynamics.

• Stability: A state of the system is considered stable when it returns to its original state after (small) disturbances. If there is too much variability, the system becomes unstable (divergent) and will converge to a new stable state.

To properly assess the ultimate implications for sports and rehabilitation practice of the theory, understanding of some of the key concepts related to dynamical systems is necessary:

• Evolution over time: Dynamical systems are characterized by changes over time. It concerns not only the current state of the system but also how it evolves over time.

• Attractors: These are stable states toward which a dynamic system moves (convergence). Attractors can be points, sequences of points, or complex patterns, and they often represent the final states or stable behavioral patterns of the system.

• Trajectories: The sequence of states that a system goes through over time is referred to as the trajectory. It describes the path the system takes from a particular initial state.

• Chaotic behavior: Some dynamical systems exhibit chaotic behavior, meaning that small changes in initial conditions can have significant and unpredictable consequences in the long term. This phenomenon is often associated with complex, nonlinear systems.

• Bifurcation: This refers to the point at which a change in the parameters of a system leads to a fundamental change in the system's behavior. It can result in the emergence of new attractors or a transition to chaotic behavior.

• Feedback mechanisms: Dynamical systems can be influenced by feedback, where the output of the system is fed back as input. This can promote stability or cause instability, depending on the type of feedback.

• Complexity and nonlinearity: Dynamical systems are often complex and nonlinear, meaning that the relationship between cause and effect cannot be easily predicted. 

Where does the dynamical system theory originate from?

The dynamical system theory traces its origins back over a century. However, it wasn't until the 1980s that it was introduced into the field of movement sciences by Peter Kugler, Scott Kelso, and colleagues Thomas and Michael Turvey. This heralded an entirely new path for performance and skill acquisition. 

Traditionally, movement was viewed as the outcome of controlled processes governed by the central nervous system, i.e., the brain. However, dynamical systems theory precipitated a paradigm shift by emphasizing the complex and dynamic nature of human movement. A significant impetus for this shift came from the work of Nikolai Bernstein, a Russian neuropsychologist and movement scientist.

While Bernstein did not explicitly coin the term "dynamical system theory," he laid the groundwork for this perspective by highlighting that movement is influenced by a complex interplay of internal and external factors and that the nervous system does not control movement linearly but rather through non-linear dynamic processes.

Bernstein's ideas profoundly influenced the field of movement sciences by promoting a more holistic understanding of human movement. His work paved the way for subsequent developments in motor control theory and led to the integration of concepts from neuroscience, biomechanics, and psychology to foster a more comprehensive understanding of movement.

Why is dynamic system theory so important for sports and rehabilitation professionals?

The current training doctrine is based on the traditional concept of the organization of movement coordination, namely the idea that the brain is the central command centre of movement control. It is often assumed that conscious, brain-dominant control is a prerequisite or even a requirement for effective automated movement control. For simple movements such as those performed in laboratory studies, such as pressing buttons and grasping objects, indeed the brain may be dominant in movement control.

However, from proponents of the ecological perspective, much criticism has been directed at the generalization of this theory, as it fails to explain how flexible, complex, and high-intensity movements, common in the sports context, can occur.

The current training practice is still based on the reductionist idea that there is a predictable relationship between properties or components of the system and the behavior of the whole. A clear example is the division of performance (behavior of the whole) into strength, speed, power, endurance, balance, etc. This mindset permeates almost all facets of sports and rehabilitation, such as training methods, analysis, testing and measurement, coaching methods, exercises, cueing, etc. Based on this idea, professions have even emerged such as strength trainers, conditioning coaches, agility trainers, skills coaches, etc.

Given the substantial amount of insights suggesting that the brain cannot possibly play such a dominant role and that there is only a very limited direct, linear relationship between components and the whole, theories describing decentralized self-organization must be embraced.

In the light of dynamical system theory, it is emphasized that motor control is not only governed by central mechanisms (such as the brain) but influenced by the interaction between the central nervous system (efferent signals), the environment, and the properties of the body itself (afferent signals and self-organization). The coupling between these top-down (brain) and bottom-up (anatomy) controls must self-organize. The body acts as a "mediation agency" between the constraints from the environment and the body itself.

This provides an explanation for the fact that sports movements are flexible and adaptive, with the body adapting to changing conditions and requirements (constraints from the task, the environment, and the individual).

When fully embracing the complexity of the influence of this theory, it has significant implications for practice in sports and rehabilitation. It will inevitably lead to the conclusion that certain aspects, and sometimes many aspects, of classical approaches are no longer or only limitedly applicable. One way to 'test' whether something is still useful is by comparing it against the standards of as many scientific disciplines related to movement coordination as possible, including anatomy, neurophysiology, motor control, and motor learning. This way, the effect of the dynamic nature of the moving and learning human body is better integrated into a holistic training approach.

Finally, this will also have implications for the various expert domains around an athlete or team. For example, in the light of dynamic system theory, strength and conditioning training cannot be separated from skill acquisition. 

What role does dynamical systems theory play at FBS?

Dynamical systems theory plays a highly dominant role at Frans Bosch Systems (FBS), as it provides a framework to optimize self-organization for improving performance and preventing and rehabilitating injuries. Frans Bosch has translated important aspects of this theory into sports training and rehabilitation, making it applicable in practice.

For instance, he has made significant progress in defining attractors, phase transitions, bifurcations, and other aspects of the complex, nonlinear behavior of coordination. While many of these are still speculative, they are based on scientific insights that show little to no contradictions in the aforementioned scientific disciplines. His translation of dynamic systems theory into movement control and learning processes is being increasingly taught and researched at universities worldwide.

Although dynamic systems theory plays a very dominant role in FBS thinking, there are many other theories that play a crucial role. For example, dynamical systems theory is viewed within a larger framework of Ecological Dynamics, which explores and models the emerging relationship between the athlete and their environment. The connections with other theories are further explored in Frans' books. 

Practical implications for training and rehabilitation

Both the book "Strength Training And Coordination" and "Anatomy Of Agility" delve deeply into the role of dynamic systems theory in movement and skill acquisition. Studying these books provides a solid foundation for further exploring the practical implications for training and rehabilitation.

This practical translation is manifested in the FBS courses. It is important to mention that attending these courses is essential for properly implementing the exercises from the FBS Exercise App. Merely copying the superficial form of the exercises without a deep understanding of the theories underlying them within the FBS framework will not lead to desired adaptations and transfers. 

Literature

Button, C., Seifert, L., Chow, J. Y., Davids, K., & Araujo, D. (2020). Dynamics of skill acquisition: An ecological dynamics approach. Human Kinetics Publishers.

Clark, J. E. (1995). On becoming skillful: Patterns and constraints. Research quarterly for exercise and sport, 66(3), 173-183.

Kelso, J. S., Holt, K. G., Kugler, P. N., & Turvey, M. T. (1980). 2 on the concept of coordinative structures as dissipative structures: II. empirical lines of convergence. In Advances in Psychology (Vol. 1, pp. 49-70). North-Holland.

Kelso, J. S. (2022). On the coordination dynamics of (animate) moving bodies. Journal of Physics: Complexity, 3(3), 031001.

Kugler, P. N., Kelso, J. S., & Turvey, M. T. (1980). 1 on the concept of coordinative structures as dissipative structures: I. theoretical lines of convergence. In Advances in psychology (Vol. 1, pp. 3-47). North-Holland.

Latash, M. L., Bernstein, N. A., & Turvey, M. T. (2014). Dexterity and its development. Psychology Press.

Newell, K. M. (1986). Constraints on the development of coordination. Motor development on children: Aspects of coordination and control.

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