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

Balamurali Ramakrishnan, Victor Kamdoum Tamba (), Hayder Natiq, Alex Stephane Kemnang Tsafack and Anitha Karthikeyan
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Balamurali Ramakrishnan: Chennai Institute of Technology
Victor Kamdoum Tamba: University of Dschang
Hayder Natiq: Imam Ja’afar Al-Sadiq University
Alex Stephane Kemnang Tsafack: University of Dschang
Anitha Karthikeyan: Prathyusha Engineering College

The European Physical Journal B: Condensed Matter and Complex Systems, 2022, vol. 95, issue 9, 1-12

Abstract: 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. Graphical abstract

Date: 2022
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DOI: 10.1140/epjb/s10051-022-00398-7

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