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Dynamical analysis of autonomous Josephson junction jerk oscillator with cosine interference term embedded in FPGA and investigation of its collective behavior in a network

  • Regular Article – Statistical and Nonlinear Physics
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Abstract

This paper reports on the dynamical analysis, field programmable gate array (FPGA) implementation of autonomous Josephson junction (JJ) jerk oscillator with cosine interference term (AJJJOCIT) and investigation of its collective behavior in a network. The AJJJOCIT derived from a resistive capacitive shunted JJ model with cosine interference term has two or no equilibrium points as a function of direct current (DC). One of the equilibrium points is unconditionally unstable and the other equilibrium point has a Hopf bifurcation where its expression depends on DC and coherence parameters. One-scroll self-excited chaotic attractor, one-scroll chaotic hidden attractor, steady state attractors, bistable periodic attractors, limit cycle and coexistence between periodic and one-scroll chaotic self-excited (or hidden) attractors are revealed in the AJJJOCIT during the numerical analysis. Moreover, the FPGA of AJJJOCIT is implemented and the FPGA results are qualitatively the same as those obtained during the numerical analysis. Finally, the collective dynamics of the AJJJOCIT are studied using a single-layer matrix of the AJJJOCIT. It is demonstrated that chimera states exist in the system and when increasing coupling strength, a completely synchronized network is revealed.

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Data availability statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: All the information was given in the paper to generate the results in the paper; there is no need for the deposited data].

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Acknowledgements

This work is partially funded by the Center for Nonlinear Systems, Chennai Institute of Technology, India via funding number CIT/CNS/2021/RD/064.

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Authors and Affiliations

  1. Center for Nonlinear Systems, Chennai Institute of Technology, Chennai, Tamilnadu, 600069, India

    Balamurali Ramakrishnan

  2. Department of Telecommunication and Network Engineering, IUT-Fotso Victor of Bandjoun, University of Dschang, P.O. Box 134, Bandjoun, Cameroon

    Victor Kamdoum Tamba

  3. Information Technology College, Imam Ja’afar Al-Sadiq University, Baghdad, 10001, Iraq

    Hayder Natiq

  4. Research Unit of Condensed Matter of Electronics and Signal Processing, Department of Physics, Faculty of Sciences, University of Dschang, PO Box 67, Dschang, Cameroon

    Alex Stephane Kemnang Tsafack

  5. Department of Electronics Engineering, Prathyusha Engineering College, Chennai, India

    Anitha Karthikeyan

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  1. Balamurali Ramakrishnan
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Contributions

BR and VKT developed the model and theoretically analyzed the rate equations of the proposed model. AK and HN did the digital implementation of the proposed model. ASKT participated in the data analysis at different stages. All authors contributed to the interpretation of the results and writing of the manuscript.

Corresponding author

Correspondence to Victor Kamdoum Tamba.

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Ramakrishnan, B., Tamba, V.K., Natiq, H. et al. Dynamical analysis of autonomous Josephson junction jerk oscillator with cosine interference term embedded in FPGA and investigation of its collective behavior in a network. Eur. Phys. J. B 95, 145 (2022). https://doi.org/10.1140/epjb/s10051-022-00398-7

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