On the periodic solutions in one dimensional cellular nonlinear networks based on Josephson Junctions (JJ's)

V.M. Mladenov; A. Slavova

doi:10.1109/CNNA.2006.341637

On the periodic solutions in one dimensional cellular nonlinear networks based on Josephson Junctions (JJ's)

V.M. Mladenov, A. Slavova

Integrated Circuits

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

2 Citations (Scopus)

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Abstract

In this paper we consider an autonomous one dimensional cellular nonlinear network (CNN) that consists of chain of N simple cells based on Josephson Junctions (JJ's) coupled by linear inductors. In fact the subject is the well known Josephson Transmission Line (JTL) that is used in many applications in superconductor electronics and more especially in Rapid Single Flux Quantum (RSFQ) technique. When the last cell is connected with the first one a ring of Josephson Junctions is formed. Using the framework of the cellular nonlinear network we consider the JTL under the umbrella of the system theory. Based on describing functions method we rigorously prove the existence and stability of periodic solutions in the cellular nonlinear network model considered. The results are confirmed by simulations.

Original language	English
Title of host publication	Proc. 2006 10th IEEE International Workshop on Cellular Neural Networks and their Applications, CNNA 2006, 28 August 2006 through 30 August 2006, Istanbul
Editors	V. Tavsanoglu, S. Arik
Place of Publication	Piscataway
Publisher	Institute of Electrical and Electronics Engineers
Pages	235-240
ISBN (Print)	1-4244-0640-4
DOIs	https://doi.org/10.1109/CNNA.2006.341637
Publication status	Published - 2006
Event	conference; CNNA 2006, Istanbul, Turkey, 28-30 Augustus 2006 - Duration: 1 Jan 2006 → …

Conference

Conference	conference; CNNA 2006, Istanbul, Turkey, 28-30 Augustus 2006
Period	1/01/06 → …
Other	CNNA 2006, Istanbul, Turkey, 28-30 Augustus 2006

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10.1109/CNNA.2006.341637

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Mladenov, V. M., & Slavova, A. (2006). On the periodic solutions in one dimensional cellular nonlinear networks based on Josephson Junctions (JJ's). In V. Tavsanoglu, & S. Arik (Eds.), Proc. 2006 10th IEEE International Workshop on Cellular Neural Networks and their Applications, CNNA 2006, 28 August 2006 through 30 August 2006, Istanbul (pp. 235-240). Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/CNNA.2006.341637

Mladenov, V.M. ; Slavova, A. / On the periodic solutions in one dimensional cellular nonlinear networks based on Josephson Junctions (JJ's). Proc. 2006 10th IEEE International Workshop on Cellular Neural Networks and their Applications, CNNA 2006, 28 August 2006 through 30 August 2006, Istanbul. editor / V. Tavsanoglu ; S. Arik. Piscataway : Institute of Electrical and Electronics Engineers, 2006. pp. 235-240

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title = "On the periodic solutions in one dimensional cellular nonlinear networks based on Josephson Junctions (JJ's)",

abstract = "In this paper we consider an autonomous one dimensional cellular nonlinear network (CNN) that consists of chain of N simple cells based on Josephson Junctions (JJ's) coupled by linear inductors. In fact the subject is the well known Josephson Transmission Line (JTL) that is used in many applications in superconductor electronics and more especially in Rapid Single Flux Quantum (RSFQ) technique. When the last cell is connected with the first one a ring of Josephson Junctions is formed. Using the framework of the cellular nonlinear network we consider the JTL under the umbrella of the system theory. Based on describing functions method we rigorously prove the existence and stability of periodic solutions in the cellular nonlinear network model considered. The results are confirmed by simulations.",

author = "V.M. Mladenov and A. Slavova",

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booktitle = "Proc. 2006 10th IEEE International Workshop on Cellular Neural Networks and their Applications, CNNA 2006, 28 August 2006 through 30 August 2006, Istanbul",

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address = "United States",

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Mladenov, VM & Slavova, A 2006, On the periodic solutions in one dimensional cellular nonlinear networks based on Josephson Junctions (JJ's). in V Tavsanoglu & S Arik (eds), Proc. 2006 10th IEEE International Workshop on Cellular Neural Networks and their Applications, CNNA 2006, 28 August 2006 through 30 August 2006, Istanbul. Institute of Electrical and Electronics Engineers, Piscataway, pp. 235-240, conference; CNNA 2006, Istanbul, Turkey, 28-30 Augustus 2006, 1/01/06. https://doi.org/10.1109/CNNA.2006.341637

On the periodic solutions in one dimensional cellular nonlinear networks based on Josephson Junctions (JJ's). / Mladenov, V.M.; Slavova, A.
Proc. 2006 10th IEEE International Workshop on Cellular Neural Networks and their Applications, CNNA 2006, 28 August 2006 through 30 August 2006, Istanbul. ed. / V. Tavsanoglu; S. Arik. Piscataway: Institute of Electrical and Electronics Engineers, 2006. p. 235-240.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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T1 - On the periodic solutions in one dimensional cellular nonlinear networks based on Josephson Junctions (JJ's)

AU - Mladenov, V.M.

AU - Slavova, A.

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N2 - In this paper we consider an autonomous one dimensional cellular nonlinear network (CNN) that consists of chain of N simple cells based on Josephson Junctions (JJ's) coupled by linear inductors. In fact the subject is the well known Josephson Transmission Line (JTL) that is used in many applications in superconductor electronics and more especially in Rapid Single Flux Quantum (RSFQ) technique. When the last cell is connected with the first one a ring of Josephson Junctions is formed. Using the framework of the cellular nonlinear network we consider the JTL under the umbrella of the system theory. Based on describing functions method we rigorously prove the existence and stability of periodic solutions in the cellular nonlinear network model considered. The results are confirmed by simulations.

AB - In this paper we consider an autonomous one dimensional cellular nonlinear network (CNN) that consists of chain of N simple cells based on Josephson Junctions (JJ's) coupled by linear inductors. In fact the subject is the well known Josephson Transmission Line (JTL) that is used in many applications in superconductor electronics and more especially in Rapid Single Flux Quantum (RSFQ) technique. When the last cell is connected with the first one a ring of Josephson Junctions is formed. Using the framework of the cellular nonlinear network we consider the JTL under the umbrella of the system theory. Based on describing functions method we rigorously prove the existence and stability of periodic solutions in the cellular nonlinear network model considered. The results are confirmed by simulations.

U2 - 10.1109/CNNA.2006.341637

DO - 10.1109/CNNA.2006.341637

M3 - Conference contribution

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BT - Proc. 2006 10th IEEE International Workshop on Cellular Neural Networks and their Applications, CNNA 2006, 28 August 2006 through 30 August 2006, Istanbul

A2 - Tavsanoglu, V.

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PB - Institute of Electrical and Electronics Engineers

CY - Piscataway

T2 - conference; CNNA 2006, Istanbul, Turkey, 28-30 Augustus 2006

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Mladenov VM, Slavova A. On the periodic solutions in one dimensional cellular nonlinear networks based on Josephson Junctions (JJ's). In Tavsanoglu V, Arik S, editors, Proc. 2006 10th IEEE International Workshop on Cellular Neural Networks and their Applications, CNNA 2006, 28 August 2006 through 30 August 2006, Istanbul. Piscataway: Institute of Electrical and Electronics Engineers. 2006. p. 235-240 doi: 10.1109/CNNA.2006.341637

On the periodic solutions in one dimensional cellular nonlinear networks based on Josephson Junctions (JJ's)

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