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MathGroup Archive 1993

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Help me

  • To: mathgroup at yoda.physics.unc.edu
  • Subject: Help me
  • From: neurox.cu!bosch at ceniai.cu (Jorge Bosch)
  • Date: Thu, 11 Feb 93 11:30:55 -0500

Hello, Mathgroup:

I am new at Mathematica. 

I'm introducing this framework in my scientific group but I'm having
trouble with it.

I have installed 2.1 version of Mathematica under Windows, on an Acer 1100sx 
computer (16 MHz, 4 MBytes Extended Memory, 80387 Numerical Coprocessor), 
MSDOS Operating System.

I am trying to solve a differential equation system (the Hoodgking and Huxley
model for a neuron) but different solutions appear at different times and 
sometimes the computer crashes. Additionally, I can't reproduce the solution 
that I got with the same system programmed in Turbo Pascal.

I enclose a copy of the non autonomous and non linear differential
equation system (four equations) as I am using. I will really appreciate if
someone could help me to find out what is wrong in my system.


Thanks in advance
Jorge Bosch


a1[v_]:=0.1 (25-v)/(Exp[(25-v)/10]-1)
b1[v_]:=4 Exp[-v/18]
a2[v_]:=0.07 Exp[-v/20]
b2[v_]:=1/(Exp[(30-v)/10]+1)
a3[v_]:=0.01 (10-v)/(Exp[(10-v)/10]-1)
b3[v_]:=0.125 Exp[-v/80]

c1oo[v_]:=a1[v]/(a1[v]+b1[v])
c2oo[v_]:=a2[v]/(a2[v]+b2[v])
c3oo[v_]:=a3[v]/(a3[v]+b3[v])

i[t_]:=If[t>=0.5 && t<=7.55,130,0]

rm=35.4;
cm=1;
gnax=120;
gkx=36;
glx=0.3;
vna=115;
vk=-12;
vl=11;

Plot[i[t],{t,0,10},PlotPoints->100]
 
NDSolve[{v'[t]==-(gnax m[t]^3 h[t] (v[t]-vna) +
         gkx n[t]^4 (v[t]-vk) + glx (v[t]-vl) + v[t]/rm - i[t]),
         m'[t]==a1[v[t]](1-m[t])-b1[v[t]] m[t],
	n'[t]==a2[v[t]](1-n[t])-b2[v[t]] n[t],
	h'[t]==a3[v[t]](1-h[t])-b3[v[t]] h[t],
	v[0]==0,
	m[0]==c1oo[0],
	n[0]==c2oo[0],
	h[0]==c3oo[0]},
	{v[t],n[t],m[t],h[t]},{t,0,10}]	

Plot[Evaluate[v[t]/.%],{t,0,10},PlotPoints->100];







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