HR_SNIC.ode

## Hindmarsh and Rose Model with adaptation and timescale factors phi and eps
## SNIC noadap bif from I=30 to -10
## SNIC adap bif from I=100 to -100
## SNIC I=0.1852, 3, 6,9 from z=30 to -30



## all parameters are taken fron HR paper, 1984.

par I0=-10.0, I1=5.0, tstart=2000
par xbar=-1.11, s=22
par a=1, b=3.5, c=1, d=5.5, eps=0.0005, phi=0.1
par theta=0

I = I0 + heav(t - tstart)*(I1 - I0)

## Initial conditions

init x = -1.5647
init y = -12.5121
init z = -10.0628


## Differential equations
## time is in ms, so multiply frequency by 1000 for Hz
## x, y, and z non-dimensional
 
x' = y - a*(x - theta)*(x - theta)*(x - theta) + b*x*x + I - z
y' = phi*(c - d*x*x - y)
z' = eps*(s*(x - xbar) - z)

## Numerical and plotting parameters

@ meth=cvode, bound=100000000, tol=1.0e-7, rtol=1.0e-7, dt=0.2, total=6000, maxstor=100000
@ xp=t, yp=x, xhi=6000, ylo=-2, yhi=4

done