Dynamical Systems And Chaos: Strange Attractors Summary

These are videos form the online course ‘Introduction to Dynamical Systems and Chaos’ hosted on Complexity Explorer. With these videos 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.

[@simpleandobvious]

To a layperson, this is super clear! Thanks!
P.s. Also, really like your lo-fi slides: there's something quite engaging in seeing an index finger point to something rather than a cursor (maybe it's hardwired into the brain!)

[@indochinapatriot435]

Well done!. Thanks.🤙

[@PabloPerroPerro]

What a brilliant explanation, thank you!

[@dawid_dahl]

Extremely interesting. Thank you.

[@HKHasty]

Love this! Thx for sharing your knowledge. Its invaluable indeed

[@basedland]

great video!

[@evyborov]

Thank you, well explained

[@linfangwang6724]

Helpful, Thanks !

[@dawid_dahl]

Have you seen the television series Devs? If so, what did you think of it? It deals predictions.

[@philippococktube]

Tank you for this!

[@directoryerror6653]

If I choose one initial condition A, how am I to know if another initial condition is a future state of A?

[@immuslum7754]

thanks a lot sir , very helpfullllllllllll :) :)

[@xNecromancerxxx]

I’m just here trying to figure out what the hell Ian Malcolm was talking about….