دانشگاه صنعتي اميركبير دانشكده مهندسي پزشكي. آشوب و بررسی آن در سیستم های بیولوژیکی. ارائه راحله داودی استاد دكتر فرزاد توحيدخواه دی 1388. What is talked in this seminar: Introduction to chaos Chaos properties History Fractals Chaos and stochastic process Logistic Map.
دانشگاه صنعتي اميركبير
دانشكده مهندسي پزشكي
آشوب و بررسی آن در سیستم های بیولوژیکی
دكتر فرزاد توحيدخواه
Poincare &Three body problem
The problem is to determine the possible motions of three point masses m1,m2,and m3, which attract each other according to Newton's law of inverse squares.
In 1977, Mitchell Feigenbaum published the noted article “ Quantitative Universality for a Class of Nonlinear Transformations", where he described logistic maps. Feigenbaum notably discovered the universality in chaos, permitting an application of chaos theory to many different phenomena.
Edward Lorenzwhose interest in chaos came about accidentally through his work on weather prediction in 1961.
The flapping of a single butterfly's wing today produces a tiny change in the state of the atmosphere. Over a period of time, what the atmosphere actually does diverges from what it would have done. So, in a month's time, a tornado that would have devastated the Indonesian coast doesn't happen. Or maybe one that wasn't going to happen, does.
(Ian Stewart, Does God Play Dice? The Mathematics of Chaos, pg. 141)
History of Fractals
The father of fractals: Gaston Julia. 1900
There were some other works out there, such as Sierpinski’s triangle and Koch’s curve.
Mandelbrot 1970 :Mandelbrot Set.
Self Similarity in Chaos
x(n) = RND
x(n+1) = 3.95 x(n) [1-x(n)]
Structure in state space
Biological models producing chaos
Applying chaos theory to a cardiac arrhythmia
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