Bifurcation diagrams

Public resources and restricted materials are identified below. Access information.

Core Readings

Terman. An introduction to dynamical systems and neuronal dynamics. Introduction & One Dimensional Equations, pp. 21-28.

Core Readings

• Bifurcation Diagrams of Scalar ODEs. Chapter 16 of Cellular Biophysics and Modeling: A primer on the systems biology of excitable cells. [DOI]
• Terman pp. 21-28 An introduction to dynamical systems and neuronal dynamics (Introduction & One Dimensional Equations).
• ODE | Slope Fields. [YouTube]

Slides & Notes

• Lecture slides — restricted PDF

• Supplementary slides: Linear Stability and Bifurcations — restricted PDF

Recordings & Tutorials

• ODE | Phase diagrams. [YouTube]

• ODE | Bifurcation Diagram. [YouTube]

Tutorial: Saddle-node bifurcation

Tutorial: Transcritical bifurcation

Tutorial: Supercritical pitchfork bifurcation

Practice

• Supplementary exercises — restricted PDF

Further Reading & Resources

• Steve Strogatz’ lecture on “One dimensional Systems” (Cornell Math Department). [YouTube]

• What is a saddle-node bifurcation? [YouTube]

• What is a transcritical bifurcation? [YouTube]

• What is a pitchfork bifurcation? [YouTube]

Restricted reading copies in the PDF companion — private repository access required.

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