标题： 同调分岔对双谐波标准映射中驱动模式相移的依赖性 显示英文标题

标题： Isochronous bifurcations dependence on the driving mode phase shift in two-harmonic standard maps

摘要： 一些非线性耦合系统的动力学性质可以通过二谐波标准映射来描述，这是一种具有两个参数的二维面积保持系统，在这种系统中，两种不同的任意共振模式相互竞争。通常情况下，假设共振模式的初始相位为零。在本文中，我们考虑这两种形成系统的竞争等时模式之间存在非零相位偏移的情况。我们观察到非零相位偏移会改变相空间，从而改变固定点的稳定性和位置。此外，相位偏移可以改变主导模式，并在主要模式之间创建中间模式。最后，我们分析了相位偏移对相空间中次级无剪切曲线出现的影响。因此，不同的相位偏移会导致相空间中次级无剪切曲线出现的各种情形。 显示英文摘要

摘要： Some dynamical properties of nonlinear coupled systems can be described by the two-harmonic standard map, a two-dimensional area-preserving system with two parameters, where two distinct arbitrary resonant modes compete. Usually, the initial phase of the resonant modes is considered to be null. In this paper, we consider a non-null phase shift between the two competing isochronous modes that form the system. We observe that a non-zero phase shift alters the phase space, changing the stability and positions of the fixed points. Furthermore, the phase shift can change the dominant mode and create intermediate modes between the main ones. Lastly, we analyze the effect of the phase shift on the onset of secondary shearless curves in the phase space. Thus, different phase shifts result in various scenarios in which secondary shearless curves emerge in the phase space.