###########################################################
#        Fitzhugh Nagumo Travelling wavefront
#
#             v_t = d v_xx + f(v) - w  
#             w_t = e (u- g v)
#
#        Stimulus is constant pulse current I(x,t) applied at right
#        end, i.e.,
#
#             v_x(0,t) = 0        
#             v_x(1,t) = I(x,t)
#
#
#        i.e., stimulus is short pulse starting at time t0 of duration
#        dt at x=1.
#
#
###########################################################
SPACE x
TIME t
SET DELTA_T=.1
SET TFINAL=.5
SET GRID=100
SET PLOTVAR=v
SET BUFSIZE=2000
SET RGB=1
SET LENGTH=1
SET METHOD=1
SET FAST=1
SET NOUT=160
#
#     default parameter values (left neumann)
#
PAR ia=1,t0=1,ddt=0.7,x0=0.5,ddx=0.05
PAR d=0.0005,eps=0.1,a=10,gam=0,del=0.1
#
#     axon initially at rest: v(x,0)=w(x,0)=0
#
CVAR v=0
CVAR w=0
#
#    boundary conditions (neumann)
#
BDRY v 0 leaky {1} {0} {0}
BDRY v 1 leaky {1} {0} {ia*(tanh((t-t0)/del)-tanh((t-t0-dt)/del))}
#
#   function definitions. 
#
FUN  f  1 a*v*(1-v)*(v-0.3)
#
#    PDE definition
#
v'=d*v_xx+f(v)-w
w'=eps*(v-gam*w)
DONE