Nonlinear dynamics and synchronization of an excited Josephson junction

Volume 18, Issue 4, pp 225--238 https://dx.doi.org/10.22436/jnsa.018.04.01

Publication Date: May 29, 2025 Submission Date: March 03, 2025 Revision Date: April 01, 2025 Accteptance Date: April 16, 2025

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Authors

G. F. Pomalegni - École de Génie Rural, Université Nationale d’Agriculture, Kétou, Bénin. M. A. Kakpo - Laboratoire de la Mécanique des Fluides, de la Dynamique Nonlinéaire et de la Modélisation des Systèmes Biologiques (LMFDNMSB), Institut de Mathématiques et de Sciences Physiques, Porto-Novo, Bénin. C. H. Miwadinou - Laboratoire de la Mécanique des Fluides, de la Dynamique Nonlinéaire et de la Modélisation des Systèmes Biologiques (LMFDNMSB), Institut de Mathématiques et de Sciences Physiques, Porto-Novo, Bénin.

Abstract

This work studies the non-harmonic dynamics of the \textbf{RCLSJ} (resistively, capacitively and inductively shunted junction) model of the Josephson junction shunted by a negative conductance and by a multi-periodic pulse source which shares the same frequency as the excitation current. The negative conductance is in series with the \textbf{RCLSJ} model of the Josephson junction which has a non-harmonic parameter and the whole is coupled to a source multi-periodic pulse in line with an inductive circuit with internal resistance. The multi-periodic pulse source is used so that the oscillations of the excitation current do not weaken over time and to compensate for the energy losses occurring during each period. The fixed points of the system are determined and are analyzed from the differential equations which govern its dynamics. The mode of operation of this model depends of the frequency of the multi-periodic pulse source pulsation and the thermodynamic properties of the junction. Alignment of system signals to maintain timing is achieved for a range of multi-periodic pulse source pulsation values and negative conductance voltage values using the backstepping technique. A complete study of the circuit studied is done digitally to detect new bifurcations and pathways leading to chaos. The contribution of the negative conductance and the multi-periodic pulse is also analyzed.

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Keywords

• Bifurcation and chaos
• Josephson junction
• internal resistance
• multi-periodic pulse
• intermittency
• synchronization

MSC

•  34C28
•  34C15
•  34D06
•  37C75

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