Writing an ODE file

To simulate this in XPPAUT we must create an ODE file which has information such as the number of equations, the parameters, initial conditions, names of variables and function definitions. The following file does the trick:

# passive membrane with step function current: passive.ode
dV/dt = (1000*(E-V)/R_M + I_0*f(t))/C_M
V(0)=-70
# I in microamps/cm^2 C_m in microfarads/cm^2 R_M in Ohm cm^2 E in mV
# t in msecs
parameter R_M=10000, C_m=1, I_0=2, E=-70
parameter t_on=5, t_off=10
# define a pulse function
f(t)=heav(t_off-t)*heav(t-t_on)
# track the current
aux ibar=f(t)*I_0
done

There is little explanation needed except for the following points:

• heav(t) is the Heaviside step function which is 0 for t<0 and 1 for t>0. Thus f(t) is a pulse function which turns on at t=t_on and turns off at t=t_off.
• V(0)=-70 is the initial condition.
• aux means that what follows is something that we want to plot but does not satisfy a differential equation.
• XPPAUT is case insensitive so upper and lower cases are synonymous.
• # means that what follows is a comment.
• param ... defines parameters
• dV/dt = ... tells XPPAUT that this is a differential equation
• done tells the parser the file is done.

Notes: (1) All the declarations at the beginning of each line can be abbreviated to their first letter; all others are ignored until a space is encountered. (2) Variables, functions, and parameters can have up to 9 letters. (3) There are at most 300 differential equations allowed, 200 parameters, and 50 functions.