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Course Co-ordinated by IIT Kharagpur
Coordinators
 
Prof. S. Banerjee
IIT Kharagpur

 

Untitled Document

The course covers lessons in Representations of Dynamical Systems,Vector Fields of Nonlinear Systems, Limit Cycles, The Lorenz Equation, The Rossler Equation and Forced Pendulum, The Chua's Circuit, Discrete Time Dynamical Systems, The Logistic Map and Period doubling, Flip and Tangent Bifurcations, Intermittency Transcritical and pitchfork, Two Dimensional Maps, Mandelbrot Sets and Julia Sets, Stable and Unstable Manifolds ,The Monodromy Matrix and the Saltation Matrix .

S.No
Topic

1

Representations of Dynamical Systems

2

Vector Fields of Nonlinear Systems

3

Limit Cycles

4

The Lorenz Equation - I

5

The Lorenz Equation - II

6

The Rossler Equation and Forced Pendulum

7

The Chua's Circuit

8

Discrete Time Dynamical Systems

9

The Logistic Map and Period doubling

10

Flip and Tangent Bifurcations

11

Intermittency Transcritical and pitchfork

12

Two Dimensional Maps

13

Bifurcations in Two Dimensional Maps

14

Introduction to Fractals

15

Mandelbrot Sets and Julia Sets

16

The Space Where Fractals Live

17

Interactive Function Systems

18

IFS Algorithms

19

Fractal Image Compression

20

Stable and Unstable Manifolds

21

Boundary Crisis and Interior Crisis

22

Statistics of Chaotic Attractors

23

Matrix Times Circle : Ellipse

24

Lyapunov Exponent

25

Frequency Spectra of Orbits

26

Dynamics on a Torus

27

Analysis of Chaotic Time Series

28

Lyapunou Function and Centre Manifold Theory

29

Non-Smooth Bifurcations

30

Normal from for Piecewise Smooth 2D Maps

31

Bifurcations in Piecewise Linear 2D Maps

32
Multiple Attractor Bifurcation and Dangerous
33

Dynamics of Discontinuous Maps

34

Introduction to Floquet Theory

35

The Monodromy Matrix and the Saltation Matrix

36

Control of Chaos

   
   
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