A nontypical route to chaos of a two-degree-of-freedom vibro-impact system is investigated. That is, the period-doubling bifurcations, and then the system turns out to the stable quasi-periodic response while the period 4-4 impact motion fails to be stable. Finally, the system converts into chaos through phrase locking of the corresponding four Hopf circles or through a finite number of times of torus-doubling.

1.
Shaw
,
J.
, and
Shaw
,
S. W.
,
1989
, “
The Onset of Chaos in a Two-degree-Freedom Impacting System
,”
ASME J. Appl. Mech.
,
56
, pp.
168
174
.
2.
Luo
,
G. W.
, and
Xie
,
J. H.
,
1998
, “
Hopf Bifurcation of a Two-Degree-of-Freedom Vibrato Impact System
,”
J. Sound Vib.
,
213
, No.
3
, pp.
391
408
.
3.
Xie
,
J. H.
,
1996
, “
Codimension Two Bifurcations and Hopf Bifurcations of an Impacting Vibrating System
,”
Appl. Math. Mech.
,
17
, pp.
65
75
.
4.
Car, J., 1981, Applications of Center Manifold Theory (Applied Mathematical Sciences 35), Springer-Verlag, New York, pp. 33–36.
5.
Iooss, G., 1987, Forms normales d’applications: Caracte´risation globale et me´thode de calcul, Universite de Nice, Nice, France.
6.
Elphick
,
C.
,
Tirapegui
,
E.
,
Brachet
,
M.
,
Coullet
,
P.
,
Iooss
,
G.
,
1987
, “
A Simple Global Characterization for Normal Forms of Singular Vector Fields
,”
Physica D
,
29
, pp.
95
127
.
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