A GEOMETRIC MODEL FOR THE DUFFING OSCILLATOR
1993 ◽
Vol 03
(03)
◽
pp. 685-691
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Keyword(s):
A geometric model for the Duffing oscillator is constructed by analyzing the unstable periodic orbits underlying the chaotic attractors present at particular parameter values. A template is constructed from observations of the motion of the chaotic attractor in a Poincaré section as the section is swept for one full period. The periodic orbits underlying the chaotic attractor are found and their linking numbers are computed. These are compared with the linking numbers from the template and the symbolic dynamics of the orbits are identified. This comparison is used to validate the template identification and label the orbits by their symbolic dynamics.
2012 ◽
Vol 22
(01)
◽
pp. 1230001
2011 ◽
Vol 468
(2137)
◽
pp. 288-302
◽
1988 ◽
Vol 80
(6)
◽
pp. 923-928
◽
Keyword(s):
1998 ◽
Vol 08
(05)
◽
pp. 1013-1023
1993 ◽
Vol 03
(02)
◽
pp. 411-429
◽