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.