Coexisting attractors may arise from many different sources such as hidden basins of attraction or peculiarly organized bifurcation structures. By exploiting the regions of mismatched bifurcations between the system and its fixed points, this study investigates coexisting attractors in a six-dimensional extension of the Lorenz system. This six-dimensional extension takes into account additional physical ingredients, namely, rotation and density-affecting scalar, which are not considered in the original Lorenz system. These newly considered physical ingredients can influence the bifurcation structures and thus the system’s characteristics with regard to coexisting attractors. Once the potential regions of coexisting attractors are identified in the parameter spaces, the coexistence of periodic and point attractors and that of two different periodic orbits in addition to the well-known coexistence of chaos and stability are demonstrated through the solution trajectories and attractor basin boundaries.

中文翻译：

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物理扩展 Lorenz 系统中的共存吸引子

共存吸引子可能来自许多不同的来源，例如隐藏的吸引盆或特殊组织的分叉结构。通过利用系统与其不动点之间不匹配的分岔区域，本研究研究了洛伦兹系统的六维扩展中的共存吸引子。这个六维扩展考虑了额外的物理成分，即旋转和影响密度的标量，这些在原始洛伦兹系统中没有考虑。这些新考虑的物理成分可以影响分叉结构，从而影响系统在共存吸引子方面的特性。一旦在参数空间中识别出共存吸引子的潜在区域，