Multirhythmic Bursting
An online resource to accompany the following paper:
RJ Butera, Jr. "Multirhythmic Bursting." CHAOS (1998) 8:274-284.
First of all, the errata!
- The parameter wphi is not specified in the appendix, it should be set to 0.067.
- The parameter kc should be 5e-4, not 5e-5.
If you would like to reproduce these simulations, you can use the file below, which is designed for use with the dynamical system software package XPP.
- chaos98.ode The XPP ODE file which has the 4 variable bursting model from the above paper.
- XPP A link to Bard Ermentrout's homepage, which has information on obtaining and installing XPP, both Windows and UNIX versions.
To reproduce the 4 coexisting bursting solutions shown in the paper (Figure 5), use the following initial conditions with taus=529 ms. Note that some parts of the paper specify taus=529.1 ms -- I have obtained multistable solutions at both values -- I think the ones at 529 had greater stability when the maps were calculated. The periodic solutions are best viewed in the (c,s) state space. It is very important to integrate using the CVODE routine with absolute and relative tolerances of 1e-8 or better, or you will not obtain all the solutions.
| Solution | V(0) | w(0) | s(0) | c(0) |
|---|---|---|---|---|
P1, 5 action potentials/burst |
-4.872564e+01 |
3.177711e-03 |
3.755320e-01 |
2.573909e-01 |
Chaotic, 4 APs/burst |
-4.703336e+01 |
4.262259e-03 |
4.333450e-01 |
2.872353e-01 |
Chaotic, 3 APs/ burst |
-4.750319e+01 |
4.055506e-03 |
4.217661e-01 |
2.903770e-01 |
Chaotic, 2 APs/burst |
-4.662822e+01 |
4.802513e-03 |
4.366877e-01 |
2.985915e-01 |
Need help? Email me at robert.butera@ece.gatech.edu