标题： 冰期循环的慢-快古气候模型中的振荡 显示英文标题

标题： Oscillations in a Slow-Fast Paleoclimate Model for Glacial Cycles

摘要： 本文研究了更新世冰期循环的Saltzman-Maasch模型的一个确定性变体，该模型被表述为一个三维动力系统，在大气二氧化碳方程中具有三次反馈。 在将模型简化为临界流形上的二维系统后，我们进行了详细的分岔分析，并识别出Hopf分岔和Bautin（广义Hopf）分岔，这些分岔控制着稳定和不稳定极限环的出现。 为了分析全局转变，我们对时间和变量进行了重新缩放，以推导出一个主导阶的哈密顿系统。 这种简化使得能够显式构造同宿轨道，并应用Melnikov方法来评估其在扰动下的持久性。 分析结果进一步得到了数值模拟的验证。 显示英文摘要

摘要： This paper investigates a deterministic variant of the Saltzman-Maasch model for Pleistocene glacial cycles, formulated as a three-dimensional dynamical system with cubic feedback in the atmospheric carbon dioxide equation. After reducing the model to a planar system on a critical manifold, we perform a detailed bifurcation analysis and identify both Hopf and Bautin (generalized Hopf) bifurcations, which govern the emergence of stable and unstable limit cycles. To analyze global transitions, we perform a rescaling of time and variables to derive a leading-order Hamiltonian system. This reduction enables the explicit construction of homoclinic orbits and the application of Melnikov's method to assess their persistence under perturbations. The analytical findings are further corroborated by numerical simulations.