**PHY ****611: ****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*:

- Steven H. Strogatz,
*Nonlinear Dynamics and Chaos with Applications to Physics, Biology, Chemistry and Engineering* - Edward Ott,
*Chaos in dynamical systems (Cambridge University Press)* - R. C. Hilborn,
*Chaos and Nonlinear Dynamics (Cambridge Univ. Press. 1994)* - M. Lakshmanan and S. Rajasekar,
*Nonlinear dynamics: Integrability Chaos and Patterns (Springer)*

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