I am using the FitzHugh-Nagumo model to perform some simulations concerning neuronal networks dynamics. The model equations are:
$\frac{dv}{dt}=a_3^3v^3+a_2v^2+a_1v+bw+I\\ \frac{dw}{dt}=1/\tau(v-w)$
When I try to numerically integrate these equations, for several set of parameters ($a_1,a_2,a_3,b,I$) and initial data $(v_0,w_0)$, the method does not converge to any solution. In particular, I am using ode45 (and ode15s) in Matlab. The message is:
Unable to meet integration tolerances without reducing the step size below the smallest value allowed (3.552714e-15) at time t
Do you have any idea about what could be the problem? It would be solved? Do this means that the solution does not exist?
Thank you very much in advance!