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Homoclinic chaos in a pair of parametrically-driven coupled SQUIDs

Agaoglou, M and Rothos, VM and Susanto, H (2014) Homoclinic chaos in a pair of parametrically-driven coupled SQUIDs. In: UNSPECIFIED, ? - ?.

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Abstract

© Published under licence by IOP Publishing Ltd. 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.

Item Type: Conference or Workshop Item (UNSPECIFIED)
Additional Information: Published proceedings: Journal of Physics: Conference Series
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science and Health > Mathematical Sciences, Department of
Depositing User: Jim Jamieson
Date Deposited: 09 Jul 2015 10:42
Last Modified: 17 Aug 2017 17:36
URI: http://repository.essex.ac.uk/id/eprint/14083

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