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What do you know about the dynamical systems theory?

It seems interesting and I want to study a sociology or astronomy application of it.
#mathematics #sociology #astronomy #astrophysics #cosmology

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Nattakarn’s Answer

Hello, Emel

Please see what I found about the Dynamic System Theory from the link below. I also provided some more details about the Sociology, Physicists and Astronomers career for your reference.

Link to the
https://en.wikipedia.org/wiki/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.

This theory deals with the long-term qualitative behavior of dynamical systems, and studies the nature of, and when possible the solutions of, the equations of motion of systems that are often primarily mechanical or otherwise physical in nature, such as planetary orbits and the behaviour of electronic circuits, as well as systems that arise in biology, economics, and elsewhere. Much of modern research is focused on the study of chaotic systems.

This field of study is also called just dynamical systems, mathematical dynamical systems theory or the mathematical theory of dynamical systems.


Sociologist:

https://www.bls.gov/ooh/life-physical-and-social-science/sociologists.htm

How to Become a Sociologist
Sociologists
Many sociology programs offer opportunities to gain experience through internships or by preparing reports.
Most sociology jobs require a master’s degree or Ph.D. Many bachelor’s degree holders find positions in related fields, such as social services, education, or public policy.

Education
Sociologists typically need a master’s degree or Ph.D. There are two types of sociology master’s degree programs: traditional programs and applied, clinical, and professional programs. Traditional programs prepare students to enter a Ph.D. program. Applied, clinical, and professional programs prepare students to enter the workplace, teaching them the necessary analytical skills to perform sociological research in a professional setting.

Courses in research methods and statistics are important for candidates in both master’s and Ph.D. programs. Many programs also offer opportunities to gain experience through internships or by preparing reports for clients.

Other Experience
Candidates with a bachelor’s degree may benefit from internships or volunteer work when looking for entry-level positions in sociology or a related field. These types of opportunities give students a chance to apply their academic knowledge in a professional setting and develop skills needed for the field.

Important Qualities
Analytical skills. Sociologists must be able to examine data and other information, often using statistical methods to test their theories.

Communication skills. Sociologists need strong communication skills when they conduct interviews, collaborate with colleagues, and write and present research results.

Critical-thinking skills. Sociologists design research projects and collect, process, and analyze information to draw logical conclusions about society and various groups of people.

Pay:
Sociologists
Median annual wages, May 2019

Sociologists
$83,420

Social scientists and related workers
$80,220

Total, all occupations
$39,810

The median annual wage for sociologists was $83,420 in May 2019. The median wage is the wage at which half the workers in an occupation earned more than that amount and half earned less. The lowest 10 percent earned less than $46,920, and the highest 10 percent earned more than $141,770.

In May 2019, the median annual wages for sociologists in the top industries in which they worked were as follows:

State government, excluding education and hospitals $92,460
Research and development in the social sciences and humanities 91,840
Educational services; state, local, and private 63,310
Most sociologists work full time during regular business hours.

Physicists and Astronomers:
https://www.bls.gov/ooh/life-physical-and-social-science/physicists-and-astronomers.htm

What Physicists and Astronomers Do
Physicists and astronomers study the ways in which various forms of matter and energy interact.

Work Environment
Physicists and astronomers spend much of their time working in offices, but they also conduct research in laboratories and observatories. Most physicists and astronomers work full time.

How to Become a Physicist or Astronomer
Physicists and astronomers typically need a Ph.D. for jobs in research and academia. However, physicist jobs in the federal government typically require a bachelor’s degree in physics. After receiving a Ph.D. in physics or astronomy, many researchers seeking careers in academia begin in temporary postdoctoral research positions.

Pay
The median annual wage for astronomers was $114,590 in May 2019.

The median annual wage for physicists was $122,850 in May 2019.

Job Outlook
Overall employment of physicists and astronomers is projected to grow 7 percent from 2019 to 2029, faster than the average for all occupations.
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Kyeremateng’s Answer

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 Systems Theory (DST) is a theory of motor development that can be applied to the management of children with Cerebral Palsy (CP; Darrah & Bar 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.

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.

DST can be used as a framework to guide intervention with many children who have motor challenges. In this review, DST will be considered as a framework to guide intervention for children with CP.
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Maria’s Answer

Hi Emel!

To be honest I had to look it up just to make sure exactly what dynamical systems theory was. I am a sociologist and I never learned about it as a undergrad student. It wasn't until I did my master in foresight that I got to learn about systems thinking in general, and even then the content that gets more into this was very little. In my experience learning more about systems thinking allowed me to first, recognize that I had always thought this way, and second provided me the tools and language to communicate how I perceived the world around me.

Maria recommends the following next steps:

1. I would suggest to start by reading Systems 1: https://www.goodreads.com/book/show/3276301-systems-one
2. Start going through some tools and resources from the Waters Center for Systems Thinking: https://waterscenterst.org/
3. Than move one to this guide that illustrates concepts from Systems 1 and goes deeper in how they could be applied to education: https://knowledgeworks.org/resources/education-changemakers-guidebook-systems-thinking/
4. If you are still into it, now you are ready to read Thinking in Systems: https://www.goodreads.com/book/show/3828902-thinking-in-systems
5. Finally this is my one recommendation that gets the closest to dynamical systems theory in my opinion but is still accessible: https://www.goodreads.com/en/book/show/40798.Turtles_Termites_and_Traffic_Jams
Thank you comment icon Thank you, that is really helpful! Emel
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