Many investigations illustrated that secondary responses coexist with primary responses in nonautonomous systems. The secondary responses are subharmonic outputs that do not bifurcate from the primary responses. In this study, a coalescence of the primary responses and the secondary responses in a coupled asymmetric system is found. A subharmonic orbit of the primary responses coalesces with a subharmonic orbit of the secondary responses via a saddle-node bifurcation in a specific parameter range. To analyze the coalescence of the responses, periodic orbits and subharmonic orbits are detected by using the shooting method and the frequency responses are obtained through the harmonic balance method. Besides, the stability of the obtained orbits is performed using the Floquet theory. The analytical results demonstrate that the new phenomenon occurs in the nonautonomous system.
|Number of pages||12|
|Journal||Physics Letters, Section A: General, Atomic and Solid State Physics|
|State||Published - 10 Dec 2001|
- Period doubling
- Subharmonic orbit