Long-term behavior of solutions of the equation \dotφ+ \sinφ=f with periodic f and the modeling of dynamics of overdamped Josephson junctions: Unlectured notes

Details Long-term behavior of solutions of the equation \dotφ+ \sinφ=f with periodic f and the modeling of dynamics of overdamped Josephson junctions: Unlectured notes Long-term behavior of solutions of the equation \dotφ+ \sinφ=f with periodic f and the modeling of dynamics of overdamped Josephson junctions: Unlectured notes

2005-12-17

arxiv.org/abs/math-ph/0512058v1

Physics

Mathematical Physics

47 pages, 23 figures

Scientific paper

The method of efficient description of long-term behavior of solutions of the non-linear first order ODE \dot\phi+\sin\phi=f for arbitrary periodic $f$ is discussed. The criterion enabling one to separate and identify the qualitatively different solutions is established. The applications of the method to the modeling of dynamics of overdamped Josephson junctions in superconductors are outlined.

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