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<p>To demonstrate the initial effect of the Josephson junction (JJ) on a linear dynamical system, this study proposes a novel four-dimensional JJ-based dynamical system (4D-JJDS). It is achieved by embedding the JJ into a three-dimensional linear dynamical system. The equilibrium set and its stability are theoretically analyzed. By means of multiple numerical methods, the hybrid bifurcation dynamics dependent on the parameter and initial state of the JJ is studied, and the dynamical behaviors dependent on the initial states of all four state variables are inspected. The results show that the stability of the equilibrium set is manifested as a periodic distribution along the JJ initial state, thereby generating an infinite variety of heterogeneous and homogeneous coexisting attractors, namely, heterogeneous and homogeneous extreme multi-stabilities. Finally, an analog circuit is designed and an FPGA hardware device is developed. Based on these, the PSIM simulations and the FPGA experiments well validate the numerical findings.</p>

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Heterogeneous and homogeneous extreme multi-stabilities in Josephson junction-based dynamical system

  • 期刊论文

  • 发表日期：

    2026年2月27日

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  • Bocheng Bao,
  • Qingwen Han,
  • Han Bao,
  • Xi Zhang,
  • Huagan Wu

摘要

To demonstrate the initial effect of the Josephson junction (JJ) on a linear dynamical system, this study proposes a novel four-dimensional JJ-based dynamical system (4D-JJDS). It is achieved by embedding the JJ into a three-dimensional linear dynamical system. The equilibrium set and its stability are theoretically analyzed. By means of multiple numerical methods, the hybrid bifurcation dynamics dependent on the parameter and initial state of the JJ is studied, and the dynamical behaviors dependent on the initial states of all four state variables are inspected. The results show that the stability of the equilibrium set is manifested as a periodic distribution along the JJ initial state, thereby generating an infinite variety of heterogeneous and homogeneous coexisting attractors, namely, heterogeneous and homogeneous extreme multi-stabilities. Finally, an analog circuit is designed and an FPGA hardware device is developed. Based on these, the PSIM simulations and the FPGA experiments well validate the numerical findings.