PH41009: Order And Chaos
| PH41009 | |||||||||||||||||||||||||||
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| Course name | Order And Chaos | ||||||||||||||||||||||||||
| Offered by | Physics | ||||||||||||||||||||||||||
| Credits | 3 | ||||||||||||||||||||||||||
| L-T-P | 3-0-0 | ||||||||||||||||||||||||||
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| Semester | Spring | ||||||||||||||||||||||||||
Syllabus
Syllabus mentioned in ERP
Flows on the line and circle: introduction; fixed points and stability; linear stability analysis; classification of linear systems; potentials; physical examples including uniform and nonuniform oscillator; overdamped pendulum. Flows in two-dimension: phase plane; phase portraits; existence, uniqueness and topological consequences; index theory; fixed points and linearization; limit cycles; Poincare-Benedixon theorem; weakly nonlinear oscillators. Bifurcations: saddle-node bifurcation; transcritical bifurcation; pitchfork bifurcation; imperfect bifurcations; Hopf bifurcations; Poincare maps. Chaos and fractals: various routes; Lorenz equations: simple properties; strange attractor; Liapunov exponent; applications of chaos; Cantor set; dimension of self-similar fractals; box dimension; correlation dimensions. One-dimensional maps: fixed points; logistic map; numerics and analysis; universality and experiments; computer based problems.