We consider self-pulsing in lasers with a gain section and an absorber section via a mechanism known as [Formula: see text]-switching, as described mathematically by the Yamada ordinary differential equation model for the gain, the absorber and the laser intensity. More specifically, we are interested in the case that gain and absorber decay on different time-scales. We present an overall bifurcation structure by showing how the two-parameter bifurcation diagram in the plane of pump strength versus decay rate of the gain changes with the ratio between the two decay rates. In total, there are ten cases BI to BX of qualitatively different two-parameter bifurcation diagrams, which we present with an explanation of the transitions between them. Moroever, we show for each of the associated eleven cases of structurally stable phase portraits (in open regions of the parameter space) a three-dimensional representation of the organization of phase space by the two-dimensional manifolds of saddle equilibria and saddle periodic orbits.The overall bifurcation structure provides a comprehensive picture of the observable dynamics, including multistability and excitability, which we expect to be of relevance for experimental work on [Formula: see text]-switching lasers with different kinds of saturable absorbers.

中文翻译：

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自脉冲激光器的 Yamada 模型：增益和吸收体不同衰减时间的分岔结构

我们考虑通过称为 [公式：见文本] 切换的机制在具有增益部分和吸收体部分的激光器中进行自脉冲，如 Yamada 常微分方程模型对增益、吸收体和激光强度的数学描述。更具体地说，我们对增益和吸收器在不同时间尺度上衰减的情况感兴趣。我们通过展示泵浦强度与增益衰减率平面中的两参数分叉图如何随两个衰减率之间的比率变化来呈现整体分叉结构。总共有 10 种情况 BI 到 BX 的定性不同的两参数分岔图，我们对它们之间的转换进行了解释。此外，