含无损传输线的约瑟夫森结电磁系统中的分岔与混沌

 建立了含无损传输线的约瑟夫森结电磁系统左端点处电压正向行波分量的一维Poincaré映射模型，运用非线性动力学理论分析了映射定点的稳定性。通过数值计算得到了映射随电压反射系数变化的分岔图，详细分析了系统随参数变化的动态演化过程。结果表明在一定参数条件下，该电磁系统中存在着分岔、混沌、周期吸引子共存、混沌吸引子共存以及周期与混沌吸引子共存等复杂的非线性动力学行为。

Bifurcation and Chaos in Josephson Junction Electromagnetic System with Lossless Transmission Line

A one-dimensional Poincaré map for the forward traveling voltage wave at the left end of Josephson junction electromagnetic system with lossless transmission line is derived. The stability at fixed point of the map is analyzed based on nonlinear dynamics theory. The bifurcation diagrams with voltage reflex coefficient as parameter are obtained through numerical computation and the dynamic evolutive process of the system is analyzed in detail. Numerical results show that under certain parametric condition complex nonlinear dynamical behaviors exist in the electromagnetic system, such as bifurcation, chaos, coexisting periodic attractors, coexisting chaotic attractors, and coexisting periodic-chaotic attractors.