@article{f71c663e941c411ca7263f32aae84f03,
title = "Homoclinic chaos in coupled SQUIDs",
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.",
keywords = "Homoclinic chaos, Melnikov theory, SQUIDs",
author = "M. Agaoglou and Rothos, {V. M.} and H. Susanto",
note = "Funding Information: M.A. thanked Professor Ron Lifshitz for fruitful discussions. The work of M.A. has been co-financed from resources of the operational program “Education and Lifelong Learning” of the European Social Fund and the National Strategic Reference Framework (NSRF) 2007-2013 within the framework of the Action State Scholarships Foundation's (IKY) mobility grants programme for the short term training in recognized scientific/research centers abroad for candidate doctoral or postdoctoral researchers in Greek universities or research centers. The work of V.R. has been co-financed by the European Union (European Social Fund ESF) and Greek national funds through the Operational Program “Education and Lifelong Learning” of the National Strategic Reference Framework (NSRF) Research Funding Program D.534 MIS: 379337: THALES Investing in knowledge society through the European Social Fund. V.R and M.A acknowledge support from FP7, Marie Curie Actions, People, International Research Staff Exchange Scheme (IRSES-606096). H.S. is supported by the Engineering and Physical Sciences Research Council (Grants No. EP/M024237/1). Publisher Copyright: {\textcopyright} 2017 Elsevier Ltd",
year = "2017",
month = jun,
day = "1",
doi = "10.1016/j.chaos.2017.04.003",
language = "British English",
volume = "99",
pages = "133--140",
journal = "Chaos, Solitons and Fractals",
issn = "0960-0779",
publisher = "Elsevier Ltd",
}