Limit cycles for extended bistable stochastic resonance system |
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| Institution: | 1. Universidad Autónoma de Baja California, Facultad de Ingeniería, Arquitectura y Diseño, Ensenada, Baja California, México;2. OSRAM, Research and Development Division, Wilmington, EE. UU., MA, United States;1. Oak Ridge National Laboratory, PO Box 2008 Oak Ridge, TN 37831, USA;2. General Atomics, PO Box 85608, San Diego, CA 92186-5608, USA;3. Oak Ridge Associated Universities, Oak Ridge, TN 37831, USA;4. Lawrence Livermore National Laboratory, PO Box 808, Livermore, CA 94550, USA;5. University of Toronto Institute for Aerospace Studies, 4925 Dufferin St, Toronto M3H 5T6, Canada;6. Sandia National Laboratory, P.O. Box 5800, Albuquerque, NM 87185, USA |
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| Abstract: | Bistable system is a typical model in stochastic resonance (SR) researching. And it has been known that the deterministic dynamics of a noised system plays an important role in making SR phenomena occur. By embedding a non-autonomous system onto a cylinder, or extending the one-dimensional non-autonomous system as a three-dimensional autonomous system restricted on a cylinder, this paper theoretically analyzes the dynamics of the well-known periodically driven bistable system. After three limit cycles (equivalent to the periodic states of the un-extended system) are proved existent for subthreshold case, they are shown to be preserved even in the suprathreshold case with large driving frequency. Moreover, it is also proved in suprathreshold case that the three ones keep touching each other and combine into one larger globally stable limit cycle as the driving frequency decreases to some certain degree. |
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