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ODE, solving the fitzhugh-nagumo equations

• To: mathgroup at smc.vnet.net
• Subject: [mg68573] ODE, solving the fitzhugh-nagumo equations
• From: "Capet Arthur" <Arthur.Capet at student.ulg.ac.be>
• Date: Wed, 9 Aug 2006 23:57:27 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

Hello,

I got to proceed a work about the FitzHugh-Nagumo elements (two of them
coupled repulsively). The problem is that i have to finish it quickly and
i got some memory troubles about how to solve numerically differential
equations.

Here is the equations for the two neurons, coupled repulsively.

 u1'[t] == u1[t](u1[t]-[Alpha]) (1-u1[t]) - v1[t] + K/2(u2[t]-u1[t]) ,

   v1'[t] == [Tau](u1[t] - [Gamma]v1[t])

 u2'[t] == u2[t](u2[t]-[Alpha]) (1-u2[t]) - v2[t] + K/2(u1[t]-u2[t]) ,

   v2'[t] == [Tau](u2[t] - [Gamma]v2[t])

the idea is to appreciate the shape of the solution for different
parameters value, and to depaint the parameter space with each
respectively solution behavior. I got no problem for that part, but if
someone could help me for the equations solving, it would be really great.