What is dynamical systems theory?
Dynamical systems theory is an interdisciplinary theory that combines many different theories, including chaos theory and catastrophe theory. Chaos is a seemingly random and completely unpredictable behavior. Statistically, chaos and randomness are not different.
What is dynamic systems theory in social work?
Dynamic systems theory focuses on the bottom-up interrelationship between smiles and other constituents of social interactions. This theoretical approach focuses on the temporal dynamics of smiles and positive emotional processes.
What are dynamic systems?
Technically, a dynamic system is a formal system the state of which depends on its state at a previous point in time. Dynamic systems are self-regulating, meaning that they are the result of the interaction of variables, and processes, which combine spontaneously to achieve a stable state or equilibrium.
What are dynamical systems?
Dynamical systems is the branch of mathematics devoted to the study of systems governed by a consistent set of laws over time such as difference and differential equations. The emphasis of dynamical systems is the understanding of geometrical properties of trajectories and long term behavior.
Definition
Dynamic systems is a theoretical framework that is used to understand and predict self-organizing phenomena in complex systems that are constantly changing, reorganizing, and progressing over time. Often mathematical formulae are used to capture processes of change within a given system.
Introduction
The term “dynamic systems” is used to refer to a variety of phenomena in nonliving and living systems that display nonlinear behavioral changes over time.
Who developed the dynamic systems theory?
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. 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.
What is dynamical systems theory?
Dynamical systems theory is an area of mathematics used to describe the behavior of complex dynamical systems, usually by employing differential equations or difference equations. When differential equations are employed, the theory is called continuous dynamical systems. From a physical point of view, continuous dynamical systems is a generalization of classical mechanics, a generalization where the equations of motion are postulated directly and are not constrained to be Euler–Lagrange equations of a least action principle. When difference equations are employed, the theory is called discrete dynamical systems. When the time variable runs over a set that is discrete over some intervals and continuous over other intervals or is any arbitrary time-set such as a Cantor set, one gets dynamic equations on time scales. Some situations may also be modeled by mixed operators, such as differential-difference equations .
What is the branch of mathematics that studies dynamical systems with an invariant measure and related problems?
Ergodic theory. Ergodic theory is a branch of mathematics that studies dynamical systems with an invariant measure and related problems. Its initial development was motivated by problems of statistical physics.
What is the point of Sharkovskii's theorem?
Sharkovskii's theorem is an interesting statement about the number of periodic points of a one-dimensional discrete dynamical system. Even simple nonlinear dynamical systems often exhibit seemingly random behavior that has been called chaos.
What is the focus of chaos theory?
Dynamical systems theory and chaos theory deal with the long-term qualitative behavior of dynamical systems. Here, the focus is not on finding precise solutions to the equations defining the dynamical system (which is often hopeless), but rather to answer questions like "Will the system settle down to a steady state in the long term, and if so, what are the possible steady states?", or "Does the long-term behavior of the system depend on its initial condition?"
What is continuous dynamical system?
From a physical point of view, continuous dynamical systems is a generalization of classical mechanics, a generalization where the equations of motion are postulated directly and are not constrained to be Euler–Lagrange equations of a least action principle. When difference equations are employed, the theory is called discrete dynamical systems.
How is a dynamical system determined?
A dynamical system has a state determined by a collection of real numbers, or more generally by a set of points in an appropriate state space. Small changes in the state of the system correspond to small changes in the numbers. The numbers are also the coordinates of a geometrical space—a manifold. The evolution rule of ...
What is Dynamic Systems Theory?
Dynamic Systems Theory (DST) is a theory of motor development that can be applied to the management of children with Cerebral Palsy (CP; Darrah & Bartlett, 1995). It is especially useful in the understanding of how movement develops and changes (Smith & Thelen, 1993), and can provide insight into a child's readiness to acquire new motor abilities. This theory proposes that movement is produced from the interaction of multiple sub-systems within the person, task and environment (Thelen, 1989). All of the sub-systems spontaneously self-organize, or come together and interact in a specific way, to produce the most efficient movement solution for each specific task (Thelen, 1989). DST also proposes that no sub-system is most important in this process (Thelen, Kelso, & Fogel, 1987). Thus, clinicians need to consider and evaluate all aspects of the task, person, and environment when trying to help a child learn a new motor ability.
What is DST in therapy?
One focus of therapy is the promotion of motor abilities. DST provides a framework to help identify when a child is most ready to learn new motor abilities. DST also suggests that motor development is non-linear, and that there are "peaks and valleys". By determining clinically when a child is most ready for motor change, ...
Why is DST important for children with CP?
CP is a condition that affects movement and posture, with possible limitations in activity and participation (Rosenbaum, Paneth, Leviton, Goldstein, & Bax, 2007). Children with CP often receive rehabilitation services from the time they are diagnosed, in the first couple years of life, until adulthood. These services for children with CP and their families typically include various forms of intervention, consultation, education, and support. The goals of pediatric rehabilitation are ultimately to promote the child's safe participation in his or her home, school, and community environments, while learning functional activities (Russell, 2005). Physiotherapy intervention commonly focuses on the development and achievement of motor abilities, or the child's "capacity to perform a movement" (Bartlett & Palisano, 2000, p. 599). Functional mobility is thought to be an important outcome of physiotherapy intervention for children with CP (Tieman, Palisano, Gracely, & Rosenbaum, 2007). Physiotherapy services also aim to promote long-term health and prevent further impairments as the child grows and changes (Bartlett & Palisano, 2000).
Why is variability important?
Researchers have suggested that a certain amount of variability is important for a healthy system and allows for change in motor behaviour (Stergiou, Harbourne & Cavanaugh, 2006). These same researchers proposed that there is an "optimal" amount of variability that allows us to be flexible in our movement options and adapt to changes in tasks and environments. We also know that too much variability (instability) and too little variability (rigidity) both result in unhealthy systems that cannot adapt to change (Stergiou et al., 2006).
Is motor development linear or nonlinear?
According to DST, development is a non-linear process (Thelen, 1989). This suggests that movement is not developed in a continuous manner, at a steady rate. Rather, a small, but critical change in one sub-system can cause the whole system to shift, resulting in a new motor behaviour (Smith & Thelen, 1993). This phase shift, or transition period is critical to DST's application to motor development.
What is the main objective of dynamic systems theory?
The dynamic systems theory’s main objective seems be targeted at better understanding how the central nervous system solves the degrees of freedom problem and how this can help rehabilitation professionals offer better solutions to movement problems.
Which theory is the most accurate depiction of how the central nervous system both develops motor skills and continues to adapt?
In terms of motor control and motor development, the literature suggests that the dynamic systems theory is the most accurate depiction of how the central nervous system both develops motor skills and continues to adapt motor control through life.
How does the brain organize the movement system?
The brain organizing the movement system via synergies and whole patterns was a paradigm shift at that time. However, the innovators of this insight did not seem to abandon the fact that if isolated biomechanical function was absent, the synergy was compromised. This seems to boil down to a fundamental principle that says independence is a prerequisite to interdependence. How can we expect a bunch of joints to work together interdependently without first meeting their independent criteria for basic mobility & motor control? Just because we now know that the brain communicates better in patterns doesn’t mean isolated joint function no longer matters.
What is synergy debate?
Interestingly, one of the “debates'' you'll come across if you read more about synergies is that some argue that the idea of synergies “constricts' ' movement to only certain patterns, not allowing for variation. This is a very linear way of thinking about synergies. A more liberating and adaptable definition for synergy was recently proposed by Latash and Anson in 2006 as well as Latash et al in 2007 as they coined the term “The Principle of Motor Abundance”.
How did Bernstein solve the degrees of freedom problem?
Bernstein figured that muscle synergies were a rational idea for solving the degrees of freedom problem. To him, muscle synergies were controlled via a hierarchical system (he seemed to have adopted some perspective from the Neurodevelopment model of motor control) in that the higher levels of the CNS activate lower level neurons which then activate chains of muscles that are wired and fire together to perform a functional task like, locomotion. If we looked at motor control and degrees of freedom like a business, muscle synergies can be seen as an automation strategy for productivity. In other words, this is a clever strategy to organize the CNS in a way that simplifies and unites various degrees of freedom toward a common goal, similar to having various departments in an organization.
How reliable are synergies?
The use of these synergies could be a very reliable way to control the many degrees of freedom the body has to offer while providing an abundance of variations within these three synergies .
Why is variable repetition important in motor learning?
When it comes to motor learning, using variable repetition to reinforce motor learning and independence is critical. The dynamic systems theory highlights that variable velocity is an important contributor to the dynamics of movement. This in, my opinion, could be considered its own principle.
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Multilevels and Multicausality in The Study of Change
- The central quest of dynamic systems is to capture and understand how patterns evolve over time and transition from one mode of functioning (or state) to another. Often, pattern formation does not follow a predetermined, linear process. Biological systems, as many other systems, are complex and composed of a multitude of extremely varied elements i...
Self-Organization, Emergence of New Forms, and Nonlinearity
- How do systems transition from one mode of functioning (or state) to another? Given the intrinsic complexity of behavioral systems, with their large numbers of elements and interactions between elements, how do systems “know” how to reorganize? And how do they form stable patterns of functioning? Self-organization is the concept at core here. Systems evolve and move through dis…
Attractor as A Metaphor For States and Transitions
- Changes in patterns and self-organization create states that can be identified to describe the behaviors or patterns that are being produced by the system and its interacting elements at a given time. The word “attractor” is used to define these states in their given situations. In living organisms, observed and recurrent behaviors are called attractor states. These behaviors can b…
Embedded Multiple Timescales and Developmental Trajectories
- Most of the examples presented above corresponded to changes in behavior occurring within relatively short timescales. But what dynamic systems also brought to our understanding of change over time is that one change occurring in a system at a given moment in time (short timescale) can alter the broader developmental trajectory of the system over the more extende…
Summary
Dynamical systems theory is an area of mathematics used to describe the behavior of complex dynamical systems, usually by employing differential equations or difference equations. When differential equations are employed, the theory is called continuous dynamical systems. From a physical point of view, continuous dynamical systems is a generalization of classical mechanics, a ge…
History
The concept of dynamical systems theory has its origins in Newtonian mechanics. There, as in other natural sciences and engineering disciplines, the evolution rule of dynamical systems is given implicitly by a relation that gives the state of the system only a short time into the future.
Before the advent of fast computing machines, solving a dynamical system required sophisticated mathematical techniques and could only be accomplished for a small class of dynamical syste…
Overview
Dynamical systems theory and chaos theory deal with the long-term qualitative behavior of dynamical systems. Here, the focus is not on finding precise solutions to the equations defining the dynamical system (which is often hopeless), but rather to answer questions like "Will the system settle down to a steady state in the long term, and if so, what are the possible steady states?", or "Does the long-term behavior of the system depend on its initial condition?"
Concepts
The dynamical system concept is a mathematical formalization for any fixed "rule" that describes the time dependence of a point's position in its ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, and the number of fish each spring in a lake.
A dynamical system has a state determined by a collection of real numbers, or more generally by a
Related fields
Arithmetic dynamics is a field that emerged in the 1990s that amalgamates two areas of mathematics, dynamical systems and number theory. Classically, discrete dynamics refers to the study of the iteration of self-maps of the complex plane or real line. Arithmetic dynamics is the study of the number-theoretic properties of integer, rational, p-adic, and/or algebraic points under repeated application of a polynomial or rational function.
Applications
In sports biomechanics, dynamical systems theory has emerged in the movement sciences as a viable framework for modeling athletic performance and efficiency. From a dynamical systems 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, m…
See also
Related subjects
• List of dynamical system topics
• Baker's map
• Biological applications of bifurcation theory
• Dynamical system (definition)
Further reading
• Abraham, Frederick D.; Abraham, Ralph; Shaw, Christopher D. (1990). A Visual Introduction to Dynamical Systems Theory for Psychology. Aerial Press. ISBN 978-0-942344-09-7. OCLC 24345312.
• Beltrami, Edward J. (1998). Mathematics for Dynamic Modeling (2nd ed.). Academic Press. ISBN 978-0-12-085566-7. OCLC 36713294.
What Is Dynamic Systems Theory?
- Dynamic Systems Theory (DST) is a theory of motor development that can be applied to the management of children with Cerebral Palsy (CP; Darrah & Bartlett, 1995). It is especially useful in the understanding of how movement develops and changes (Smith & Thelen, 1993), and can provide insight into a child's readiness to acquire new motor abilities. ...
Why Is DST Important For Children with CP?
- CP is a condition that affects movement and posture, with possible limitations in activity and participation (Rosenbaum, Paneth, Leviton, Goldstein, & Bax, 2007). Children with CP often receive rehabilitation services from the time they are diagnosed, in the first couple years of life, until adulthood. These services for children with CP and their families typically include various forms …
What Do We Know About Variability?
- Researchers have suggested that a certain amount of variability is important for a healthy system and allows for change in motor behaviour (Stergiou, Harbourne & Cavanaugh, 2006). These same researchers proposed that there is an "optimal" amount of variability that allows us to be flexible in our movement options and adapt to changes in tasks and environments. We also know that t…
What Don't We Know?
- We do not know how to identify transition states clinically yet. There remain several unanswered questions about this. Are there certain clinical signs we can watch for to know when a child is about to learn new tasks, or ready to develop new abilities? We do not know how to measure variability clinically. What is considered optimal variability? How much variability is needed to ch…
How Does This Apply to Clinical Practice?
- If clinicians, parents, and researchers can determine when a child is about to experience a transition period, then according to DST, they are most ready to acquire new motor tasks. Therapy can then be provided in an intensive burst, promoting new motor abilities when the child is most ready to acquire them. This can then be followed by a rest period, during which the child can be …
Where Do We Go from Here?
- Further work is needed to understand how to identify a transition period clinically. Therapists need more clinical tools to measure variability, and guidelines around what amount of variability is optimal, and what indicates readiness to change. We also need more research to explore which factors are associated with a child's readiness to change. If we can determine these factors, we …
Summary
- Rehabilitation practitioners want to help children with CP participate in life, at home, in school, and in the community. One focus of therapy is the promotion of motor abilities. DST provides a framework to help identify when a child is most ready to learn new motor abilities. DST also suggests that motor development is non-linear, and that there are "peaks and valleys". By determ…