论文标题
冰川周期的PP04模型的周期性状态之间的放牧分叉和过渡
Grazing bifurcations and transitions between periodic states of the PP04 model for the glacial cycle
论文作者
论文摘要
我们研究地球冰川周期的周期性行为以及不同周期性状态之间的过渡时，当外部参数（例如$ω$）或内部参数（例如$ d $）变化时。我们使用气候变化的PP04模型对此进行建模。这是一个强迫不连续的Filippov（非平滑）动力学系统。定期强迫这并共存定期轨道。我们发现该系统中的过渡主要是由于放牧事件，导致了放牧分叉。对放牧分叉进行了分析，这些分叉对周期轨道的吸引力和存在区域的影响是在系统参数的各种变化下确定的。放牧过渡是PP04模型的参数（内部和外部）的一般变化的出现。我们发现该时期轨道之间的放牧过渡类似于中期过渡的轨道。
We look at the periodic behaviour of the Earth's glacial cycles and the transitions between different periodic states when either external parameters (such as $ω$) or internal parameters (such as $d$) are varied. We model this using the PP04 model of climate change. This is a forced discontinuous Filippov (non-smooth) dynamical system. When periodically forced this has co-existing periodic orbits. We find that the transitions in this system are mainly due to grazing events, leading to grazing bifurcations. An analysis of the grazing bifurcations is given and the impact of these on the domains of attraction and regions of existence of the periodic orbits is determined under various changes in the parameters of the system. Grazing transitions arise for general variations in the parameters (both internal and external) of the PP04 model. We find that the grazing transitions between the period orbits resemble those of the Mid-Pleistocene-Transition.
