This paper studies a natural mechanism, called a homoclinic-doubling cascad
e, for the disappearance of period-doubling cascades in vector fields. Simp
ly put, an entire period-doubling cascade collides with a saddle-type equil
ibrium. Homoclinic-doubling cascades are known to have self-similar structu
re. in contrast to the well-known Feigenbaum constant, the scaling constant
s for homoclinic-doubling depend on the eigenvalues of the saddle equilibri
um. Specifically, we present here for the first time a detailed study of ho
moclinic-doubling cascades in a smooth vector field, namely a three-dimensi
onal polynomial model proposed by Sandstede. A numerical algorithm is prese
nted for computing homoclinic-doubling cascades in general vector fields, w
hich makes use of the program AUTO/HoMCoNT. This allows us to compute two t
ypes of homoclinic-doubling cascades. one where the primary homoclinic orbi
t undergoes an inclination flip bifurcation and one where it undergoes an o
rbit flip bifurcation. Our results bring out the scaling constants in good
agreement with analytical estimates obtained from one-dimensional maps. (C)
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