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Random perturbations of nonlinear oscillators: Homogenization and large deviations |
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| Institution: | 1. Materials Research and Technology, Luxembourg Institute of Science and Technology, 5, av. des Hauts-Fourneaux, L-4362 Esch/Alzette, Luxembourg;2. Université Libre de Bruxelles, Belgium\nBuilding Architecture and Town Planing Department (BATir)\nAv. F. Roosevelt 50 CP165/42, 1050 Brussels Belgium;1. Department of Mechanical Engineering, University of California, Berkeley, CA, USA;2. Department of Chemical and Biomolecular Engineering, University of California, Berkeley, USA;3. Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA |
| Abstract: | This paper considers two prototypical strongly nonlinear oscillators with weak dissipation and noise: a pendulum which is acted on by a small noisy torque and opposed by a friction; and the noisy Duffing-van der Pol oscillator. But over a long time the weak dissipative and noise effects can be significant. This paper develops asymptotic techniques based on averaging and large deviations to study the effects of weak noise on the escape from the domain of attraction of stable equilibrium points and limit cycles in phase-space. |
| Keywords: | Large deviations Homogenization Duffing-van der Pol oscillator Energy harvester SMIB power system |
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