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Department of Mathematics

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.