A Note on the Dynamics of Modified rf-SQUIDs: Simulations and Possible Control over Oscillations

Nikolay Kyurkchiev, Tsvetelin Zaevski, Anton Iliev () and Todor Branzov
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Nikolay Kyurkchiev: Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 8, 1113 Sofia, Bulgaria
Tsvetelin Zaevski: Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 8, 1113 Sofia, Bulgaria
Anton Iliev: Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 24, Tzar Asen Str., 4000 Plovdiv, Bulgaria
Todor Branzov: Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 8, 1113 Sofia, Bulgaria

Mathematics, 2025, vol. 13, issue 5, 1-16

Abstract: The so-call SQUIDs (abbreviated from superconducting quantum interference device) are very sensitive apparatuses especially built for metering very low magnetic fields. These systems have applications in various practical fields—biology, geology, medicine, different engineering areas, etc. Their features are mainly based on superconductors and the Josephson effect. They can be differentiated into two main groups—direct current (DC) and radio frequency (RF) SQUIDs. Both of them were constructed in the 1960s at Ford Research Labs. The main difference between them is that the second ones use only one superconducting tunnel junction. This reduces their sensitivity, but makes them significantly cheaper. We investigate namely the rf-SQUIDs in the present work. A number of authors devote their research to the rf-SQUIDs driven by an oscillating external flux. We aim to enlarge the theoretical base of these systems by adding new factors in their dynamics. Several particular cases are explored and simulated. We demonstrate also some specialized modules for investigating the proposed model. One application for possible control over oscillations is also discussed. It is based on the Fourier transform and, as a consequence, on the characteristic function of some probability distributions.

Keywords: homoclinic and heteroclinic bifurcations in rf SQUIDs; Melnikov function; control over oscillations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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