Editing Dynamical systems theory (section)

== Applications ==

=== In biomechanics ===
In [[sports biomechanics]], dynamical systems theory has emerged in the movement sciences as a viable framework for modeling athletic performance and efficiency. It comes as no surprise, since dynamical systems theory has its roots in [[Analytical mechanics]]. From psychophysiological perspective, the human movement system is a highly intricate network of co-dependent sub-systems (e.g. respiratory, circulatory, nervous, skeletomuscular, perceptual) that are composed of a large number of interacting components (e.g. blood cells, oxygen molecules, muscle tissue, metabolic enzymes, connective tissue and bone). In dynamical systems theory, movement patterns emerge through generic processes of self-organization found in physical and biological systems.<ref>Paul S Glazier, Keith Davids, Roger M Bartlett (2003). [http://www.sportsci.org/jour/03/psg.htm "DYNAMICAL SYSTEMS THEORY: a Relevant Framework for Performance-Oriented Sports Biomechanics Research"]. in: Sportscience 7. Accessed 2008-05-08.</ref> There is no research validation of any of the claims associated to the conceptual application of this framework.

=== In cognitive science ===
Dynamical system theory has been applied in the field of [[neurodynamics|neuroscience]] and [[cognitive science|cognitive development]], especially in [[the neo-Piagetian theories of cognitive development]]. It is the belief that cognitive development is best represented by physical theories rather than theories based on syntax and [[AI]]. It also believed that differential equations are the most appropriate tool for modeling human behavior. These equations are interpreted to represent an agent's cognitive trajectory through [[state space]]. In other words, dynamicists argue that [[psychology]] should be (or is) the description (via differential equations) of the cognitions and behaviors of an agent under certain environmental and internal pressures. The language of chaos theory is also frequently adopted.

In it, the learner's mind reaches a state of disequilibrium where old patterns have broken down. This is the phase transition of cognitive development. [[Self-organization]] (the spontaneous creation of coherent forms) sets in as activity levels link to each other. Newly formed macroscopic and microscopic structures support each other, speeding up the process. These links form the structure of a new state of order in the mind through a process called ''scalloping'' (the repeated building up and collapsing of complex performance.) This new, novel state is progressive, discrete, idiosyncratic and unpredictable.<ref>{{cite journal|title=The Promise of Dynamic Systems Approaches for an Integrated Account of Human Development|journal=Child Development|date=2000-02-25|first=Mark D.|last=Lewis|volume=71|issue=1|pages=36–43|url=http://home.oise.utoronto.ca/~mlewis/Manuscripts/Promise.pdf|access-date=2008-04-04|doi=10.1111/1467-8624.00116|pmid=10836556 |citeseerx=10.1.1.72.3668}}</ref>

Dynamic systems theory has recently been used to explain a long-unanswered problem in child development referred to as the [[A-not-B error]].<ref>{{cite journal|title=Development as a dynamic system|journal=Trends in Cognitive Sciences|date=2003-07-30|first=Linda B.|last=Smith|author2=Esther Thelen|volume=7|issue=8|pages=343–8|url=http://www.indiana.edu/~cogdev/labwork/dynamicsystem.pdf|access-date=2008-04-04|doi=10.1016/S1364-6613(03)00156-6|pmid=12907229|citeseerx=10.1.1.294.2037|s2cid=5712760}}</ref> 

Further, since the middle of the 1990s<ref>R.F. Port and T. van Gelder [eds.] (1995). Mind as Motion. Explorations in the Dynamics of Cognition. A Bradford Book. MIT Press, Cambridge/MA.</ref> [[cognitive science]], oriented towards a system theoretical [[connectionism]], has increasingly adopted the methods from (nonlinear) “Dynamic Systems Theory (DST)“.<ref>van Gelder, T. and R.F. Port (1995). It’s about time: an overview of the dynamical approach to cognition. pp. 1-43. In: R.F. Port and T. van Gelder [eds.]: Mind as Motion. Explorations in the Dynamics of Cognition. A Bradford Book. MIT Press, Cambridge/MA.</ref><ref>van Gelder, T. (1998b). The dynamical hypothesis in cognitive science. Behavioral and Brain Sciences 21: 615-628.</ref><ref>Abrahamsen, A. and W. Bechtel (2006). Phenomena and mechanisms: putting the symbolic, connectionist, and dynamical systems debate in broader perspective. pp. 159-185. In: R. Stainton [ed.]: Contemporary Debates in Cognitive Science. Basil Blackwell, Oxford.</ref> A variety of neurosymbolic cognitive neuroarchitectures in modern connectionism, considering their mathematical structural core, can be categorized as (nonlinear) dynamical systems.<ref>Nadeau, S.E. (2014). Attractor basins: a neural basis for the conformation of knowledge. pp. 305-333. In: A. Chatterjee [ed.]: The Roots of Cognitive Neuroscience. Behavioral Neurology and Neuropsychology. Oxford University Press, Oxford.</ref><ref>Leitgeb, H. (2005). Interpreted dynamical systems and qualitative laws: from neural network to evolutionary systems. Synthese 146: 189-202.</ref><ref>Munro, P.W. and J.A. Anderson. (1988). Tools for connectionist modeling: the dynamical systems methodology. Behavior Research Methods, Instruments, and Computers 20: 276-281.</ref> These attempts in neurocognition to merge connectionist cognitive neuroarchitectures with DST come from not only neuroinformatics and connectionism, but also recently from [[developmental psychology]] (“Dynamic Field Theory (DFT)”<ref>Schöner, G. (2008). Dynamical systems approaches to cognition. pp. 101-126. In: R. Sun [ed.]: The Cambridge Handbook of Computational Psychology. CambridgeUniversity Press, Cambridge.</ref><ref>Schöner, G. (2009) Development as change of systems dynamics: stability, instability, and emergence. pp. 25-31. In: J.P. Spencer, M.S.C. Thomas, and J.L. McClelland. [eds.]: Toward a Unified Theory of Development: Connectionism and Dynamic Systems Theory ReConsidered. Oxford University Press, Oxford.</ref>) and from “[[evolutionary robotics]]” and “[[developmental robotics]]”<ref>Schlesinger, M. (2009). The robot as a new frontier for connectionism and dynamic systems theory. pp. 182-199. In: J.P. Spencer, M.S.C. Thomas, and J.L. McClelland. [eds.]: Toward a Unified Theory of Development: Connectionism and Dynamic Systems Theory ReConsidered. Oxford University Press, Oxford.</ref> in connection with the mathematical method of “[[evolutionary computation]] (EC)”. For an overview see Maurer.<ref>Maurer, H. (2021). Cognitive science: Integrative synchronization mechanisms in cognitive neuroarchitectures of the modern connectionism. CRC Press, Boca Raton/FL, chap. 1.4, 2., 3.26, 11.2.1, ISBN 978-1-351-04352-6. https://doi.org/10.1201/9781351043526</ref><ref>Maurer, H. (2016). „Integrative synchronization mechanisms in connectionist cognitive Neuroarchitectures“. Computational Cognitive Science. 2: 3. https://doi.org/10.1186/s40469-016-0010-8</ref>

===In second language development===
{{Main|Dynamic approach to second language development}}
The application of Dynamic Systems Theory to study [[second language acquisition]] is attributed to [[Diane Larsen-Freeman]] who published an article in 1997 in which she claimed that [[second language acquisition]] should be viewed as a developmental process which includes [[language attrition]] as well as language acquisition.<ref>{{cite web|url=https://academic.oup.com/applij/article-abstract/18/2/141/134192|title=Chaos/Complexity Science and Second Language Acquisition|date=1997|journal=Applied Linguistics|doi=10.1093/applin/18.2.141 |last1=Larsen-Freeman |first1=D. |volume=18 |issue=2 |pages=141–165 }}</ref> In her article she claimed that language should be viewed as a dynamic system which is dynamic, complex, nonlinear, chaotic, unpredictable, sensitive to initial conditions, open, self-organizing, feedback sensitive, and adaptive.