Overview of theoretical and numerical approaches for the study of nonlinear and chaotic dynamicsrnin science and engineering. Poincare-Bendixson theory. Floquet theory. Fractals, bifurcationrnanalysis, predictability, strange attractors, and routes to chaos. Roles of dissipation and noise inrndeterministic chaos. Use of Lyapunov spectra, fractal dimension, information, entropy, correlationrns, and attractor reconstruction to describe chaos. Chaos in iterated maps and systems ofrnnonlinear ordinary differential equations. Spatiotemporal chaos in coupled map-lattices and inrnsystems of nonlinear partial differential equations. Perturbation technique. Numerical itegration ofrnsystems of stiff equations, operator splitting, exponential time integration, spectral and pseudospectral methods.rn
Doctor of Philosophy (PhD) in Mechanical Engineering
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| content serial | Description |
|---|
| 1 | Overview , Chaos, Fractals, and Dynamics |
| 2 | One-Dimensional Flows, Flows on the Line |
| 3 | Linear Stability Analysis |
| 4 | Bifurcations |
| 5 | Flows on the Circle |
| 6 | Two-Dimensional Flows, Linear Systems |
| 7 | Phase Plane |
| 8 | Limit Cycles |
| 9 | Bifurcations Revisited. |
| 10 | Hysteresis in the Driven Pendulum and Josephson Junctionrn |
| 11 | CHAOS , Lorenz Equations |
| 12 | One-Dimensional Maps |
| 13 | Logistic Map: Analysis |
| 14 | Fractals, Countable and Uncountable Sets |
| 15 | Strange Attractorsrn |
| 16 | Final Examniation |
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