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Nonlineer Dinamik Sistemlere Giriş

İTÜ Fizik Kış Sunumu - 2 Şubat 2011

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,...)
kütle yay sistemleri (genel koordinatlar)
hava durumu dinamikleri
akışkanlar dinamiği (p,v)
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 -
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
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