# computing a homoclinic orbit
# main ODE
x'=per*y
y'=per*(x*(1-x)-a*y+s*x*y)
# auxiliary ODE for fixed point
x1'=f1
y1'=f2
# period
per'=0
# free parameter
s'=0
# right-hand sides
f1=y1
f2=x1*(1-x1)-a*y1+s*x1*y1
# are set to zero for x1,y1
b f1
b f2
# these are the eigenvalues
lamp=(-a+sqrt(a*a+4))/2
lamm=(-a-sqrt(a*a+4))/2
# project off the fixed point from unstable manifold
b x1+eps-x
b y1+eps*lamp-y
# project onto the stable manifold
b x1+eps-x'
b y1+eps*lamm-y'
# check the errors at either end
aux bx=x1+eps-x
aux by0=y1+eps*lamp-y
aux by1=y1+eps*lamm-y
par a=0,eps=.1
init per=8.1,x=.1,y=.1
@ total=1.01,meth=qualrk,dt=.001
done
x=.001
y=.0017
per=18.722
s=-1.15
a=2.0556
eps=.001