Homoclinic chaos in a pair of parametrically-driven coupled SQUIDs
3RD INTERNATIONAL CONFERENCE ON MATHEMATICAL MODELING IN PHYSICAL SCIENCES (IC-MSQUARE 2014)(2024)
Abstract
An rf superconducting quantum interference device (SQUID) consists of a
superconducting ring interrupted by a Josephson junction (JJ). When driven by
an alternating magnetic field, the induced supercurrents around the ring are
determined by the JJ through the celebrated Josephson relations. This system
exhibits rich nonlinear behavior, including chaotic effects. We study the
dynamics of a pair of parametrically-driven coupled SQUIDs arranged in series.
We take advantage of the weak damping that characterizes these systems to
perform a multiple-scales analysis and obtain amplitude equations, describing
the slow dynamics of the system. This picture allows us to expose the existence
of homoclinic orbits in the dynamics of the integrable part of the slow
equations of motion. Using high-dimensional Melnikov theory, we are able to
obtain explicit parameter values for which these orbits persist in the full
system, consisting of both Hamiltonian and non-Hamiltonian perturbations, to
form so-called Silnikov orbits, indicating a loss of integrability and the
existence of chaos.
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Key words
mechanical engineering
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