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Homoclinic chaos in coupled SQUIDs

Agaoglou, M and Rothos, VM and Susanto, H (2017) 'Homoclinic chaos in coupled SQUIDs.' Chaos, Solitons and Fractals, 99. 133 - 140. ISSN 0960-0779

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Abstract

An rf superconducting quantum interference device (SQUID) consists of a superconducting ring interrupted by a Josephson junction (JJ). The induced supercurrents around the ring are determined by the JJ through the celebrated Josephson relations. We study the dynamics of a pair of parametrically-driven coupled SQUIDs lying on the same plane with their axes in parallel. The drive is through the alternating critical current of the JJs. This system exhibits rich nonlinear behavior, including chaotic effects. 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 Shilnikov orbits, indicating a loss of integrability and the existence of chaos.

Item Type: Article
Uncontrolled Keywords: SQUIDs, Homoclinic chaos, Melnikov theory
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science and Health > Mathematical Sciences, Department of
Depositing User: Jim Jamieson
Date Deposited: 19 May 2017 15:24
Last Modified: 21 Sep 2018 14:15
URI: http://repository.essex.ac.uk/id/eprint/19474

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