Computer Codes for the Mathematical Biosciences Publication

The computer programs below are for Mathematical Biosciences, vol. 287, pp. 105-121, 2017. They are use to demonstrate techniques for fast-slow analysis. The programs run with the XPPAUT computer software. XPPAUT is free, and runs on Unix, Linux, and Windows machines. It can be downloaded from the website of Bard Ermentrout .

• A relaxation oscillator model.
  This was used in Figures 1-4. relax.ode


• Model for bursting with one slow variable.
  This was used in Figures 5-8. s-model.ode


• Model for phantom bursting with two slow variables.
  This was used in Figures 9 and 10. phantom.ode


• A 3-dimensional, dimensionless implementation of the Hodgkin-Huxley model that exhibits MMOs.
  This was used to make Figures 12 and 13. HH.ode


• A 5-dimensional implementation of a Purkinje cell model that exhibits torus canards.
  This was used to make Figures 14. torus.ode


• A 5-dimensional implementation of a Purkinje cell model that exhibits torus canards.
  This was used to make the bifurcation diagrams in Figures 15. torus_bif.ode