Melnikov’s Method at a Saddle-Node and the Dynamics of the Forced Josephson Junction
- 1 November 1987
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Mathematical Analysis
- Vol. 18 (6) , 1699-1715
- https://doi.org/10.1137/0518122
Abstract
A Version of Melnikov’s method is developed for time-periodic perturbations of a planar vector field having a separatrix loop at a saddle-node. The method is applied to the forced pendulum, or Josephson junction, equation $\beta \ddot \phi + \dot \phi + \sin \phi = \rho + \varepsilon \sin \omega t$.
Keywords
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