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

中文翻译：

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FPGA中嵌入余弦干扰项的自主约瑟夫森结加加速度振荡器的动态分析及其在网络中的集体行为研究

本文报告了具有余弦干扰项 (AJJJOCIT) 的自主约瑟夫森结 (JJ) 加加速度振荡器的动态分析、现场可编程门阵列 (FPGA) 实现以及对其在网络中的集体行为的调查。从具有余弦干扰项的电阻电容分流 JJ 模型导出的 AJJJOCIT 作为直流 (DC) 的函数具有两个或没有平衡点。其中一个平衡点是无条件不稳定的，另一个平衡点具有 Hopf 分岔，其表达式取决于 DC 和相干参数。单卷自激混沌吸引子、单卷混沌隐藏吸引子、稳态吸引子、双稳态周期吸引子、在数值分析过程中，AJJJOCIT 揭示了周期性和单卷混沌自激（或隐藏）吸引子之间的极限循环和共存。此外，实现了 AJJJOCIT 的 FPGA，其 FPGA 结果与数值分析得到的结果在定性上相同。最后，使用 AJJJOCIT 的单层矩阵研究 AJJJOCIT 的集体动力学。证明了系统中存在嵌合状态，当增加耦合强度时，会显示出一个完全同步的网络。

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