Homoclinic chaos in coupled SQUIDs
Homoclinic chaos in coupled SQUIDs
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DOI：
10.1016/j.chaos.2017.04.003
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发表时间：
2017-06
影响因子：
7.8
通讯作者：
M. Agaoglou;V. Rothos;H. Susanto
中科院分区：
文献类型：
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作者：
M. Agaoglou;V. Rothos;H. Susanto
射频超导量子干涉装置(SQUID)由一个超导环和一个约瑟夫森结(JJ)组成。环周围的感应超流是由JJ通过著名的约瑟夫森关系式确定的。我们研究了一对参数驱动的耦合SQUID的动力学，它们位于同一平面上，它们的轴是平行的。驱动是通过JJ的交流临界电流进行的。该系统表现出丰富的非线性行为，包括混沌效应。我们利用这些系统的弱阻尼特性进行多尺度分析，得到了描述系统慢动态的振幅方程。这幅图使我们能够揭示慢运动方程的可积部分的动力学中同宿轨道的存在。利用高维Melnikov理论，我们能够得到这些轨道在包含哈密顿和非哈密顿扰动的完整系统中持续存在的显式参数值，从而形成所谓的Shilnikov轨道，这表明了可积性的损失和混沌的存在。
An rf superconducting quantum interference device (SQUID) consists of a superconducting ring interrupted by a Josephson junction (JJ). The induced supercurrents around the ring are determined by the JJ through the celebrated Josephson relations. We study the dynamics of a pair of parametrically-driven coupled SQUIDs lying on the same plane with their axes in parallel. The drive is through the alternating critical current of the JJs. This system exhibits rich nonlinear behavior, including chaotic effects. We take advantage of the weak damping that characterizes these systems to perform a multiple-scales analysis and obtain amplitude equations, describing the slow dynamics of the system. This picture allows us to expose the existence of homoclinic orbits in the dynamics of the integrable part of the slow equations of motion. Using high-dimensional Melnikov theory, we are able to obtain explicit parameter values for which these orbits persist in the full system, consisting of both Hamiltonian and non-Hamiltonian perturbations, to form so called Shilnikov orbits, indicating a loss of integrability and the existence of chaos.