Introduction to Dynamical Systems and Chaos (Summer, 2016)
Lead instructor: David Feldman
https://www.complexityexplorer.org/courses/61-introduction-to-dynamical-systems-and-chaos-summer-2016
About the Course:
In this course you'll gain an introduction to the modern study of dynamical systems, the interdisciplinary field of applied mathematics that studies systems that change over time.
Topics to be covered include: phase space, bifurcations, chaos, the butterfly effect, strange attractors, and pattern formation. The course will focus on some of the realizations from the study of dynamical systems that are of particular relevance to complex systems:
1. Dynamical systems undergo bifurcations, where a small change in a system parameter such as the temperature or the harvest rate in a fishery leads to a large and qualitative change in the system's
behavior.
2. Deterministic dynamical systems can behave randomly. This property, known as sensitive dependence or the butterfly effect, places strong limits on our ability to predict some phenomena.
3. Disordered behavior can be stable. Non-periodic systems with the butterfly effect can have stable average properties. So the average or statistical properties of a system can be predictable, even if its details are not.
4. Complex behavior can arise from simple rules. Simple dynamical systems do not necessarily lead to simple results. In particular, we will see that simple rules can produce patterns and structures of surprising complexity.
Lead instructor: David Feldman
https://www.complexityexplorer.org/courses/61-introduction-to-dynamical-systems-and-chaos-summer-2016
About the Course:
In this course you'll gain an introduction to the modern study of dynamical systems, the interdisciplinary field of applied mathematics that studies systems that change over time.
Topics to be covered include: phase space, bifurcations, chaos, the butterfly effect, strange attractors, and pattern formation. The course will focus on some of the realizations from the study of dynamical systems that are of particular relevance to complex systems:
1. Dynamical systems undergo bifurcations, where a small change in a system parameter such as the temperature or the harvest rate in a fishery leads to a large and qualitative change in the system's
behavior.
2. Deterministic dynamical systems can behave randomly. This property, known as sensitive dependence or the butterfly effect, places strong limits on our ability to predict some phenomena.
3. Disordered behavior can be stable. Non-periodic systems with the butterfly effect can have stable average properties. So the average or statistical properties of a system can be predictable, even if its details are not.
4. Complex behavior can arise from simple rules. Simple dynamical systems do not necessarily lead to simple results. In particular, we will see that simple rules can produce patterns and structures of surprising complexity.
In the 1932 Annual Review of Fluid Mechanics, Horace Lamb said:
"I am an old man now, and when I die and go to heaven there are two matters on which I hope for enlightenment. One is quantum electrodynamics, and the other is the turbulent motion of fluids. And about the former I am rather optimistic."
"I am an old man now, and when I die and go to heaven there are two matters on which I hope for enlightenment. One is quantum electrodynamics, and the other is the turbulent motion of fluids. And about the former I am rather optimistic."
Statistical Physics of Adaptation
https://journals.aps.org/prx/abstract/10.1103/PhysRevX.6.021036
https://journals.aps.org/prx/abstract/10.1103/PhysRevX.6.021036
Physical Review X
Statistical Physics of Adaptation
Evolutionary adaptation is commonly thought of as arising from reproduction. A new thermodynamic perspective on self-organization far from thermal equilibrium links the biological world and other systems governed by the same general physical principles.
Network Valuation in Financial Systems
https://arxiv.org/abs/1606.05164
https://arxiv.org/abs/1606.05164
"Life is pleasant . Death is peaceful. It's the transition that is troublesome."
- Isaac Asimov
- Isaac Asimov
توی این صفحه لینکهایی وجود داره که شما با رفتن به اونها میتونید با #فرکتال ها بازی کنید و شکلهایی که دوست دارید رو بسازید. پیشنهاد میشه حتما سر بزنید:
https://www.complexityexplorer.org/courses/26-fractals-and-scaling-fall-2015/segments/3933
https://www.complexityexplorer.org/courses/26-fractals-and-scaling-fall-2015/segments/3933
Today the network of relationships linking the human race to itself and to the rest of the biosphere is so #complex that all aspects affect all others to an extraordinary degree. Someone should be studying the whole system, however crudely that has to be done, because no gluing together of partial studies of a complex nonlinear system can give a good idea of the behaviour of the whole.
Murray Gell-Mann in ISSS The Primer Project International Society for the Systems Sciences (ISSS) seminar (12 October - 10 November 1997).
Murray Gell-Mann in ISSS The Primer Project International Society for the Systems Sciences (ISSS) seminar (12 October - 10 November 1997).
Network Science is everywhere! And the list is alredy incomplete, missing CEU's fantastic Phd program: http://ow.ly/uXMQ301tHdm. See NU's PhD: http://ow.ly/l0va301hQ3b
کورسهای جدید complexity explorer:
https://www.complexityexplorer.org/news/47-june-july-update-courses-courses-courses
https://www.complexityexplorer.org/news/47-june-july-update-courses-courses-courses
گروه بیندانشگاهی «فیزیک طوری 😊» یک گروه «علمیه» که اعضای اون آدمهای باحال، با حوصله و کنجکاوی هستند که علم رو به صورت «حرفهای» دنبال میکنند.
توی این گروه هر چیزی که به فیزیک و ریاضیات مرتبط باشه فرستاده میشه، همینطور حواسمون هست موضوعاتی که «منبع موثقی» ندارند و یا مطالبی که تحت عنوان «شبهعلم» طبقهبندی میشند رو به اشتراک نذاریم.
بنابراین ما اینجا دور هم جمع شدیم تا از امکاناتی که تلگرام برامون به ارمغان اورده به توسعهی علممون کمک کنیم، کلی چیز یادیگیریم و از یادگیریمون لذت ببریم.
لینک گروه «فیزیکطوری😊»:
https://telegram.me/joinchat/BBtzwD0S6ff2F8Rz9eBJ6Q
لطفا این لینک رو برای هر کس که میفرستید، قبلش از شرایط و سیاستهای گروه آگاهش کنید. ما دوستداریم کسایی که حضور و فعالیتشون به گروه کمک میکنه در گروه حضور پیدا کنند.
راستی، ترجیح ما اینه که بحثهای خیلی طولانی در گروه نداشته باشیم. در صورت نیاز و علاقه، مباحث بحثبرانگیز رو میتونید به گروه «بحث فیزیکطوری 🎓» منتقل کنید:
https://telegram.me/joinchat/A0ATzD5lub60apbedf_1vA
توی این گروه هر چیزی که به فیزیک و ریاضیات مرتبط باشه فرستاده میشه، همینطور حواسمون هست موضوعاتی که «منبع موثقی» ندارند و یا مطالبی که تحت عنوان «شبهعلم» طبقهبندی میشند رو به اشتراک نذاریم.
بنابراین ما اینجا دور هم جمع شدیم تا از امکاناتی که تلگرام برامون به ارمغان اورده به توسعهی علممون کمک کنیم، کلی چیز یادیگیریم و از یادگیریمون لذت ببریم.
لینک گروه «فیزیکطوری😊»:
https://telegram.me/joinchat/BBtzwD0S6ff2F8Rz9eBJ6Q
لطفا این لینک رو برای هر کس که میفرستید، قبلش از شرایط و سیاستهای گروه آگاهش کنید. ما دوستداریم کسایی که حضور و فعالیتشون به گروه کمک میکنه در گروه حضور پیدا کنند.
راستی، ترجیح ما اینه که بحثهای خیلی طولانی در گروه نداشته باشیم. در صورت نیاز و علاقه، مباحث بحثبرانگیز رو میتونید به گروه «بحث فیزیکطوری 🎓» منتقل کنید:
https://telegram.me/joinchat/A0ATzD5lub60apbedf_1vA
Interdisciplinary research has consistently lower funding success
http://www.nature.com/nature/journal/v534/n7609/full/nature18315.html
http://www.nature.com/nature/journal/v534/n7609/full/nature18315.html
Introduction to Dynamical Systems and Chaos (Summer, 2016)
Lead instructor: David Feldman
https://www.complexityexplorer.org/courses/61-introduction-to-dynamical-systems-and-chaos-summer-2016/enrollment/new
Lead instructor: David Feldman
https://www.complexityexplorer.org/courses/61-introduction-to-dynamical-systems-and-chaos-summer-2016/enrollment/new
#Butterfly_effect
The "butterfly effect" is a common way to describe the sensitivity to initial conditions in a #chaotic system. It is a reference to the frequently used metaphor of a butterfly flapping its wings somewhere in the world and then much later a typhoon developing at another location as a distant, but direct, result of this.
The "butterfly effect" is a common way to describe the sensitivity to initial conditions in a #chaotic system. It is a reference to the frequently used metaphor of a butterfly flapping its wings somewhere in the world and then much later a typhoon developing at another location as a distant, but direct, result of this.