期刊
INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS
卷 54, 期 11, 页码 3960-3985出版社
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10773-014-2429-6
关键词
Oscillators; PT-symmetry; Stability; Periodic orbits
资金
- National Science Foundation [CMMI-1000337, DMS-1312856]
- FP7-People [IRSES-605096]
- US-AFOSR [FA9550-12-10332]
- Binational (US-Israel) Science Foundation [2010239]
- U.S. Department of Energy
- Dept. of Atomic Energy, Govt. of India through a Raja Ramanna Fellowship
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1312856] Funding Source: National Science Foundation
In the present work, we explore the case of a general -symmetric dimer in the context of two both linearly and nonlinearly coupled cubic oscillators. To obtain an analytical handle on the system, we first explore the rotating wave approximation converting it into a discrete nonlinear Schrodinger type dimer. In the latter context, the stationary solutions and their stability are identified numerically but also wherever possible analytically. Solutions stemming from both symmetric and anti-symmetric special limits are identified. A number of special cases are explored regarding the ratio of coefficients of nonlinearity between oscillators over the intrinsic one of each oscillator. Finally, the considerations are extended to the original oscillator model, where periodic orbits and their stability are obtained. When the solutions are found to be unstable their dynamics is monitored by means of direct numerical simulations.
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