  we consider a system with homoclinic orbit, We decompose the corresponding
variational equation on the space of solutions and provide sufficient
conditions for the permanency of homoclinic in the space of $C^1$ vector
fields. We also provide new sufficient conditions for the persistence and
multiple bifurcations of the bounded solutions nearby. our results can be
verified numerically and do not meet the limitations of classic methods (like
Melnikon integrals and Poincare map)
