Lecture 14
Square-wave bursting and homoclinic bifurcations
Public resources and restricted materials are identified below. Access information.
Core Readings
- Read the highlighted parts of Izhikevich 2000 (a review of neuronal bursting mechanisms).
You may be amazed at how much you understand about the nonlinear dynamics of neuronal activity. The three most important types of bursting are:- Square-wave bursting - also called fold/homoclinic bursting - onset is a saddle-node (fold) bifurcation, offset is a saddle homoclinic orbit bifurcation, and the fast subsystem is bistable.
- Elliptic bursting - also called subHopf/fold cycle bursting - onset is a subcritical Hopf bifurcation, offset is a fold limit cycle bifurcation, and the fast subsystem is bistable.
- Parabolic bursting - also called circle/circle bursting - onset is a SNIC bifurcation, offset is also a SNIC bifurcation, and the fast subsystem is not bistable\
- The highlighted portions of Bertram et al. 2007 on the control of insulin secretion by pancreatic beta-cells through metabolic and electrical oscillations.\
- Highlighted portions of Tabak et al. 2000 on network bursting in embryonic chick spinal cord.
Reading details
Izhikevich 2000. Neural excitability, spiking and bursting.
Bertram et al. 2007. Metabolic and electrical oscillations: partners in controlling pulsatile insulin secretion.
Tabak et al. 2000. Modeling of spontaneous activity in developing spinal cord.
Slides & Notes
Recordings & Tutorials
Tutorial: Bifurcations and bursting tutorial
Models & Demonstrations
Practice
Restricted reading copies in the PDF companion — private repository access required.