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Indian Institute of Science Education and Research Bhopal


PHY 411: Nonlinear Dynamics and Chaos (4)

Prerequisites:   PHY 305: Classical Mechanics,
                         PHY 301: Mathematical Methods I

Learning Objectives:

This course introduces fundamental concepts of dynamical systems, dynamical flows, non-linearity and chaos.

Course Contents:

Introduction to Dynamical Systems: Overview, Examples and Discussion

One-dimensional flows: Flows on the line, Fixed points and stability, Population growth, Linear stability analysis, Saddle-node, Transcritical and Pitchfork bifurcations, Flow on the circle

Two-dimensional flows: Linear system: Definitions and examples, Phase portraits, Fixed points and linearization, Limit cycles, Poincare-Bendixson theorem, Lienard systems, Bifurcations revisited: Saddle-node, Transcritical and Pitchfork bifurcations, Hopf bifurcations, Oscillating chemical reactions, Poincare maps, Global bifurcation of cycles, Coupled Oscillators and Quasiperiodicity

Chaos: Lorenz equations: Properties of Lorenz equation, Lorenz Map; One-dimensioanl map: Fixed points, Logistic map, Liapunov exponent, Fractals: Countable and Uncountable Sets, Cantor Set, Dimension of Self-Similar Fractals, Box dimension, Pointwise and Correlation Dimensions; Strange Attractors: Baker’s map, Henon map Chaos in Hamiltonian systems

Suggested Books:

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