In dynamical systems theory, an orbit corresponding to a solution
is
called homoclinic to the equilibrium point
of the dynamical system if
as
.
There are two types of homoclinic orbits with codimension 1, namely
homoclinic-to-hyperbolic-saddle (HHS), whereby
is a saddle, saddle-focus or bi-focus, and
homoclinic-to-saddle-node (HSN), whereby
is a saddle-node (i.e., exhibits a limit point
bifurcation). We recall that
AUTO has a toolbox for homoclinic continuation, named HOMCONT [4], [5].
During the continuation, it is necessary to keep track of several eigenspaces
of the equilibrium in each step. To do this in an efficient way, MATCONT
incorporates the continuation of invariant subspaces [7]
into the defining system.
Subsections