The Importance of Dynamic Systems | by Teun Thomassen

動態系統理論的重要性 | 授權翻譯自螺旋肌力體能學院Leo

Frans Bosch System Level1 國際師資認證課程：https://forms.gle/M2wJNhvH2uo9YZpL9

Apr 27, 2024

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. 

動態系統理論的重要性，在於其提供一個寶貴的架構，用以理解系統的複雜性，在一個「變化是唯一常數」的世界中，這個理論不僅增加了架構性的理解，也促進了實際應用於各種科學和應用領域，包括物理、生物學、心理學和經濟學。此外，它在與運動協調的組織和學習相關的過程中，扮演著關鍵角色，在深入探討為何這個理論對於運動和復健實務具有重要意義之前，探索動態系統和複雜系統的概念至關重要。

Dynamical systems and complex systems

動態系統和複雜系統

 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. 

 這兩個詞彙密切相關，但並非完全相同，在本文範圍之外不深入探討，但以下是我們可以應用在訓練的一些特徵：動態系統理論可以視為複雜系統理論的一個子集，專注於隨時間變化的系統的動力學，它提供分析（簡單或）複雜系統的時間行為以及了解其動力學如何從組件之間的互動中產生的工具和概念。

另一方面，複雜系統理論則提供更廣泛的框架，用於研究具有多個相互作用組件的系統的特性和行為，涵蓋動態和靜態方面。在實務上，動態系統理論經常應用於複雜系統的脈絡中，以分析系統行為的時間演變，並了解其如何從組成部分之間的互動中產生。為方便起見，在本文中，我將使用「複雜動態系統 (complex dynamical system)」這個詞，用於（經常是混沌的）運動競技的脈絡。

What is the dynamical systems theory?

什麼是動態系統理論

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.

動態系統理論是一個跨學科的理論框架，用於理解和建構系統模板的複雜，且通常是非線性動力學。如前所述，該理論應用於各個領域。在 Jane Clark 的文章中，描述了該理論的四個基本概念：

• 約束：這個概念表明運動是由圍繞系統的給定限制或設定邊界產生的。這些約束由 Karl Newell 進一步分為任務約束、個體約束和環境約束。
• 自組織：運動模式的組織自發地從約束中產生，而不是由大腦中的「小人物」發出指令。
• 模式：由系統內部元素的相互作用產生的規律、重複的結構或行為，模式表現出趨向穩定性和通常具有看似隨機和不可預測的動力學等特徵。
• 穩定性：當系統在（小）干擾後恢復到其原始狀態時，系統的狀態被認為是穩定的；如果變異太大，系統就會變得不穩定（發散），並將收斂到新的穩定狀態。

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. 

要正確評估動態系統理論對運動和復健實務的最終影響，必須先了解一些與動態系統相關的核心概念：

• 時間演變：動態系統的特徵在於時間上的變化，它不僅關心系統的當前狀態，也關心它如何隨著時間演變。
• 吸引子：這些是動態系統移動（收斂）的穩定狀態，吸引子可以是點、點序列或複雜模式，它們通常代表系統的最終狀態或穩定的行為模式。
• 軌跡：系統在一段時間內經歷的狀態序列稱為軌跡，它描述了系統從特定初始狀態所經過的路徑。
• 混沌行為：某些動態系統會表現出混沌行為，這意味著初始條件的微小變化，在長期內可能會產生顯著且難以預測的後果，這種現象通常與複雜的非線性系統相關。
• 分岔 (理論)：這指的是系統參數的變化導致系統行為發生根本性改變的點，它可能導致新吸引子的出現或轉變為混沌行為。
• 回饋機制：動態系統會受到回饋的影響，其中系統的輸出會回饋給輸入，這取決於回饋類型，可以促進穩定或造成不穩定。
• 複雜性和非線性：動態系統通常是複雜且非線性的，這意味著因果關係之間的關係不容易預測。

Where does the dynamical system theory originate from?

 動態系統理論源自哪裡？

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.

動力系統理論的起源可以追溯到一個多世紀以前。然而，直到 1980 年代，才由 Peter Kugler、Scott Kelso 和同事 Thomas 及 Michael Turvey 引入運動科學領域，這為表現和技能學習開闢了全新的途徑。

傳統上，運動被視為由中樞神經系統（即大腦）控制過程的結果，然而，動力系統理論促使了典範轉移 (paradigm shift)，強調了人類運動的複雜性和動態性，這一轉變的重要推動力來自俄羅斯神經心理學家和運動科學家Nikolai Bernstein的工作。

雖然Bernstein並未明確地創造出「動力系統理論」這個術語，但他通過強調運動受內在和外在因素的複雜相互作用影響，以及神經系統並非以線性方式控制運動，而是通過非線性動態過程來控制運動，為這種觀點奠定了基礎。

Bernstein的思想深刻地影響了運動科學領域，促進了對人類運動更全面的理解，他的工作為隨後的運動控制理論發展鋪平了道路，並導致了神經科學、生物力學和心理學概念的整合，以促進對運動的更全面理解。

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

 動態系統理論為何對運動和復健專業人員如此重要？

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. 

目前訓練原則是基於傳統的運動協調組織概念，即大腦是運動控制的中央指揮中心，人們經常認為意識、以大腦為主導的控制是有效自動化運動控制的先決條件，甚至必要條件。對於實驗室研究中所進行的簡單動作，例如按鈕和抓取物體，大腦在運動控制中確實可能占主導地位。

然而，從生態學觀點的支持者來看，許多批評都針對此理論的推廣，因為它無法解釋運動場景中常見的靈活、複雜且高強度運動是如何發生的。

目前的訓練實務仍然基於還原論 (reductionist) 的觀念，即系統的特性或組成部分與整體行為之間存在可預測的關係，一個明顯的例子是將表現（整體行為）劃分為力量、速度、功率、耐力、平衡等，這種思維方式幾乎滲透到運動和復健的各個層面，例如訓練方法、分析、測試和測量、教練方法、練習、提示等。基於這種觀念，甚至出現了專門的職業，例如力量訓練師、體能教練、敏捷性訓練師、技能教練等。

鑑於大量見解顯示大腦不可能扮演如此主導的角色，以及組成部分與整體之間只有非常有限的直接線性關係，因此必須採用描述去中心化自我組織 (decentralized self-organization) 的理論。

基於動態系統理論，強調運動控制不僅受中央機制（例如大腦）的控制，而且還受中樞神經系統（傳出訊號）、環境以及身體自身特性（傳入訊號和自組織）之間的相互作用影響。頂層（大腦）和底層（解剖學）控制之間的耦合必須自我組織，身體充當環境和身體自身約束之間的「調解機構」。

這為運動動作靈活和適應性提供了解釋，身體能夠適應不斷變化的條件和需求（來自任務、環境和個體的約束）。

當充分理解此理論的複雜影響時，它對運動和復健實務具有重大意義，這將不可避免地導致結論，即古典方法的某些方面，有時甚至是許多方面，不再適用或僅限於有限的適用範圍。測試某事物是否仍然有用的方法之一，是將其與盡可能多的與運動協調相關的科學學科（包括解剖學、神經生理學、運動控制和運動學習）的標準進行比較，通過這種方式，更能將運動和學習人類身體的動態本質整合到整體的訓練方法中。

最後，這也將對運動員或團隊周圍的各種專家領域產生影響。例如，基於動力系統理論，力量和體能訓練不能與技能習得分開。

What role does dynamical systems theory play at FBS?

動態系統理論在 FBS 中扮演什麼角色？

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. 

動態系統理論在 Frans Bosch 系統 (FBS) 中扮演著極其重要的角色，因為它提供了一個框架，用於優化自我組織以提升表現並預防及復健傷害。Frans Bosch 將此理論的重要面向轉化為運動訓練和復健，使其在實務中得以應用。

例如，他在定義吸引子、相變、分岔以及協調複雜非線性行為的其他面向方面取得了重大進展，儘管其中許多仍然存在推測性，但它們與上述科學學科中幾乎沒有矛盾的部分，他將動態系統理論轉化為運動控制和學習過程，這項知識在全球各大學日益受到教學和研究。

儘管動態系統理論在 FBS 的思考模式中扮演著非常重要的角色，但還有許多其他理論也扮演著關鍵角色，例如，動態系統理論被視為生態動力學 (Ecological Dynamics) 更廣泛框架的一部分，它探討並模擬運動員及其環境之間的新興關係。Frans 的書籍進一步探討了與其他理論的關聯性。

Practical implications for training and rehabilitation

訓練與復健的實用意義

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. 

「Strength Training And Coordination」和「Anatomy Of Agility」兩本書都深入探討動態系統理論在動作和技能習得中的角色，研讀這些書籍，為進一步探討訓練和復健的實際應用提供了堅實的基礎。

這種實務轉譯體現在 FBS 課程中，值得一提的是，參加這些課程對於正確執行 FBS 訓練應用程式中的運動至關重要，僅僅複製運動表面的形式，而沒有深入了解 FBS 架構中其背後理論，將無法達到預期的適應和轉移。

Frans Bosch System Level1 國際師資認證課程：https://forms.gle/M2wJNhvH2uo9YZpL9

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.