Order and Chaos





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Course Contents

Dynamical Systems; Nonlinear dynamics of one dimensional flows, Fixed point, linear stability analysis, bifurcations; Nonlinear dynamics of two dimensional flows, Phase space, equilibrium, Limit cycle, stability, bifurcations; Periodicity, disturbed periodicity; Nonlinear dynamics of 1D and 2D maps, fixed point, stability, Poincare section ; Routes to chaos Period doubling, quasi periodicity and intermittency, Universality, Renormalization; Measurement of chaos, Lyapunov exponent, entropy; Strange attractors, fractal geometry and fractal dimension; Examples from Sciences and Engineering.



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