MATH332 - Nonlinear Dynamics and Chaos
Unit Syllabus
- Second order differential equations in the phase plane: phase plane diagrams; autonomous systems; conservative systems; damped linear oscillator; nonlinear damping.
- Limit cycles and periodic solutions: Poincare-Bendixon criterion.
- Forced oscillations: subharmonic responses, jump phenomena, particular studies of the van der Pol equation and Duffing's equation.
- Bifurcation: transcritical, pitchfork, Hopf.
- Maps: one- and two-dimensional.
- The logistic map: periodic solutions, stability, period doubling and chaos; Lyapunov exponents.
- The "baker's map": strange attractors.
- Chaos in forced damped oscillations.