We study the dynamics of a nonlinear dissipative bosonic Josephson junction with a time-dependent sinusoidal perturbation in the interaction term. We demonstrate parametric resonance, where the system undergoes sustained periodic oscillations even in the presence of dissipation. This happens when the frequency of the perturbation is close to twice the frequency of the unperturbed Josephson oscillations and the strength of perturbation exceeds a critical threshold. We have formulated the threshold conditions for parametric oscillations. To explore the nature of the oscillations, we carry out a multiple time scale analysis of the stability boundaries in terms of the V-shaped Arnold tongue in the parameter space. Full numerical simulations have been performed for the zero-, running-, and π -phase modes of the nonlinear Josephson effect. Our results demonstrate that in the π -phase mode the system is capable of making a transition from regular parametric to chaotic param...

中文翻译：

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耗散的玻色约瑟夫森结中的参数振荡

我们在相互作用项中研究了具有时间依赖性正弦扰动的非线性耗散玻色子约瑟夫森结的动力学。我们展示了参数共振，即使在存在耗散的情况下，系统也会经历持续的周期性振荡。当摄动频率接近未摄动约瑟夫森振荡频率的两倍并且摄动强度超过临界阈值时，就会发生这种情况。我们已经制定了参数振荡的阈值条件。为了探索振荡的性质，我们根据参数空间中的V形Arnold舌对稳定性边界进行了多个时间尺度分析。已经对非线性约瑟夫森效应的零，运行和π相模式进行了完整的数值模拟。