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Nonlineer Dinamik Sistemlere Giriş

İTÜ Fizik Kış Sunumu - 2 Şubat 2011
by

Mehmet Ali Anil

on 1 February 2011

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Transcript of Nonlineer Dinamik Sistemlere Giriş

Dinamik Sistem Nedir? Nonlineer Dinamik Sistemler Mehmet Ali Anıl Zorlanmayan Dinamik Sistemler Otonom Dinamik Sistemler Otonom Lineer Dinamik Sistemler Nonlineer vs. Lineer 1 Kaos All rights reserved by yamamo2 All rights reserved by yamamo2 Çift Sarkaç Faz Uzayı 4 Boyutlu faz uzayı, nonlineer Sarkaç (sürtünme var) devreler, sinir hücreleri, (Vi,Ij)
populasyonlar (n1,n2,...)
sarkaçlar,
kütle yay sistemleri (genel koordinatlar)
hava durumu dinamikleri
akışkanlar dinamiği (p,v)
morfogenesis
Zaman
Durum Uzayı (değişkenleri)
Evrim operatörü Poincare-Bendixson Teoremi
n>3 boyutlu sistemler
nonlineer olma Nonlineer vs. Lineer 2 Limit Çevrimler Davranış Kümeleri 3 Nonlineer vs. Lineer Davranış Kümeleri 3b Nonlineer vs. Lineer çoğul
davranış bellekli -
adaptif
sistemler osilatörler 2D Nöron Modeli Fitzhugh Nagumo Modeli bir
örnek Faz uzayı Fitzhugh Nagumo Modeli I=0 Fitzhugh Nagumo Modeli Faz uzayı I=0.9 Faz uzayı I=1.45 Fitzhugh Nagumo Modeli Faz uzayı I=0.3 Fitzhugh Nagumo Modeli Dallanma Hopf Dallanması Eğer - Düğüm
Dallanması Dallanma Diren Dallanması Nonlinear Systems, Hasan Khalil
Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , Guckenheimer, Holmes Nonlinear Dynamics and Chaos , Strogatz Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting , Izhikevich
Full transcript