Description: Chaos Theory studies the behavior of dynamical systems that are highly sensitive to initial conditions. Small differences in initial conditions yield widely diverging outcomes for such dynamical systems, rendering long-term prediction impossible in general.
Curriculum
- 1 Section
- 40 Lessons
- 10 Weeks
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- Chaos, Fractals and Dynamical Systems40
- 2.1Lecture 1: Representations of Dynamical Systems
- 2.2Lecture 2: Vector Fields of Nonlinear Systems
- 2.3Lecture 3: Limit Cycles
- 2.4Lecture 4: The Lorenz Equation – I
- 2.5Lecture 5: The Lorenz Equation – II
- 2.6Lecture 6: The Rossler Equation and Forced Pendulum
- 2.7Lecture 7: The Chua’s Circuit
- 2.8Lecture 8: Discrete Time Dynamical Systems
- 2.9Lecture 9: The Logistic Map and Period doubling
- 2.10Lecture 10: Flip and Tangent Bifurcations
- 2.11Lecture 11: Intermittency Transcritical and pitchfork
- 2.12Lecture 12: Two Dimensional Maps
- 2.13Lecture 13: Bifurcations in Two Dimensional Maps
- 2.14Lecture 14: Introduction to Fractals
- 2.15Lecture 15: Mandelbrot Sets and Julia Sets
- 2.16Lecture 16: The Space Where Fractals Live
- 2.17Lecture 17: Interactive Function Systems
- 2.18Lecture 18: IFS Algorithms
- 2.19Lecture 19: Fractal Image Compression
- 2.20Lecture 20: Stable and Unstable Manifolds
- 2.21Lecture 21: Boundary Crisis and Interior Crisis
- 2.22Lecture 22: Statistics of Chaotic Attractors
- 2.23Lecture 23: Matrix Times Circle : Ellipse
- 2.24Lecture 24: Lyapunov Exponent
- 2.25Lecture 25: Frequency Spectra of Orbits
- 2.26Lecture 26: Dynamics on a Torus
- 2.27Lecture 27: Dynamics on a Torus
- 2.28Lecture 28: Analysis of Chaotic Time Series
- 2.29Lecture 29: Analysis of Chaotic Time Series
- 2.30Lecture 30: Lyapunou Function and Centre Manifold Theory
- 2.31Lecture 31: Non-Smooth Bifurcations
- 2.32Lecture 32: Non-Smooth Bifurcations
- 2.33Lecture 33: Normal from for Piecewise Smooth 2D Maps
- 2.34Lecture 34: Bifurcations in Piecewise Linear 2D Maps
- 2.35Lecture 35: Bifurcations in Piecewise Linear 2D Maps
- 2.36Lecture 36: Multiple Attractor Bifurcation and Dangerous
- 2.37Lecture 37: Dynamics of Discontinuous Maps
- 2.38Lecture 38: Introduction to Floquet Theory
- 2.39Lecture 39: The Monodromy Matrix and the Saltation Matrix
- 2.40Lecture 40: Control of Chaos
