# 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'=0
y1'=0
# 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-x)*lamp-(y1-y)
# project onto the stable manifold
zz=(x1-x')*lamm-(y1-y')
b zz
# normalization
b sqrt((x1-x)^2+(y1-y)^2)-eps
b sqrt((x1-x')^2+(y1-y')^2)-eps
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