Welcome to Prof. Roussel's Chemistry 4010/5010/7010

Nonlinear dynamics for (Bio)Chemists

• Course policies and general information:
  • Chem 4010
  • Chem 5010/7010
• Assignments and solutions
• Tests and solutions
• Lecture materials
  • Chapter 1 lecture slides: Introductory ideas
  • Chapter 2 example: Xppaut input file for the exciplex mechanism
  • Section 3.1: Linear stability analysis
    • Lecture slides
    • Notes for in-class example: Reversible exciplex mechanism
  • Section 3.2: Lyapunov functions
    • Lecture slides
    • Notes for in-class example: a chemical Lyapunov function
  • Sections 4.2, 4.3, 5.1 and 5.2: Saddle-node and transcritical bifurcations
    • Lecture slides
    • Xppaut for in-class example: photoactivated enzyme
      • Input file for bifurcation analysis
      • Input files for visualizing hysteresis: ODE file and animation script
    • Notes for in-class example: SI model of an infectious disease
  • Section 4.4: Andronov-Hopf bifurcations
    • Lecture slides
    • Notes for in-class example: Sel'kov model
    • Xppaut input file for Sel'kov model
    • Xppaut input file for Salnikov model
  • Sections 4.5 and 5.3: Period-doubling bifurcations and chaos
    • Lecture slides
    • Xppaut input file for the Willamowski-Rössler model
    • Improved Xppaut input file for the Willamowski-Rössler model
  • Chapter 6: Invariant manifolds
    • Lecture slides
    • Notes for in-class example: centre manifold of the exciplex mechanism
    • Interlude: the Lotka-Volterra model
    • Xppaut input file for the Lotka-Volterra model
    • Maple worksheet for the HIV model of section 6.5.2. Because there are few comments in this worksheet, I strongly suggest that you read this worksheet alongside the explanations in the textbook.
  • Chapter 7: Singular perturbation theory
    • Lecture slides: Introduction to singular perturbation theory and Tikhonov's theorem
    • Notes for in-class example: scaling and Tikhonov's theorem applied to an ozone decomposition model
    • Lecture slides: inner and outer solutions of singularly perturbed equations
    • Notes for in-class example: inner and outer solutions
    • Maple worksheet: global approximation to the time evolution in the ozone decomposition model
    • Notes for in-class example: geometric singular perturbation theory
    • Maple worksheet: geometric singular perturbation theory calculation of the slow manifold
  • Chapter 8: Hamiltonian systems
    • Lecture slides: Introduction to Hamiltonian systems
    • Maple worksheet: two-dimensional harmonic ion trap
    • Lecture slides: Symplectic integration methods
    • Lecture slides: Implementation of implicit integrators
    • Matlab/Octave examples (harmonic oscillator)
      • Semi-implicit Euler method
      • Hamiltonian-preserving method (iterative solution). Needs the harmonic oscillator Hamiltonian function
      • Hamiltonian-preserving method (using fsolve()). Needs the harmonic oscillator Hamiltonian function and the file defining the equations to solve
  • Chapter 10 lecture slides: Maps and differential equations
  • Chapter 11: stability and bifurcations in maps
    • Lecture slides: Fixed points, stability and bifurcations
    • Maple worksheet: analysis of the logistic map
    • Maple worksheet: sensitive dependence on initial conditions
    • Lecture slides: sensitive dependence on initial conditions
    • Matlab/Octave code to compute the Lyapunov exponent of the logistic map, function defining the logistic map and function defining the derivative of the map
• Lab materials
  • Sept. 24: Xppaut input file for the Griffith model
  • Oct. 1
    • Xppaut input file for a predator-prey model
    • Sample exam solution based on a bifurcation analysis of this model
• Useful stuff:
  • Running xppaut in Windows

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