Chemistry 5850: Nonlinear Dynamics

• Course outline and general information
• Lecture notes
  • Lecture 1
    • Definition and examples of dynamical systems
    • Introduction to phase-plane analysis
  • Lecture 2: Stability analysis for ODEs
  • Lecture 3
    • Introduction to bifurcations
    • xpp input file for the Brusselator
    • xpp input file for the autocatalator
  • Lecture 4: Bifurcation analysis using AUTO
  • Lecture 5: Invariant manifolds
  • Lecture 6
    • Singular perturbation theory
    • Sample Maple worksheet showing the computation of the Michaelis-Menten mechanism's slow manifold by geometric singular perturbation theory
  • Lecture 7: Hamiltonian systems
  • Lecture 8: Nonautonomous systems
  • Lecture 9: Maps and differential equations
  • Lecture 10
    • Stability and bifurcation analysis of maps
    • Maple worksheet demonstrating the computation of Liapunov exponents for the logistic map
  • Lecture 11: Delay-differential equations
  • Lecture 12: Reaction-diffusion equations
• Assignments

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