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We look at the periodic behaviour of the Earth's glacial cycles and thetransitions between different periodic states when either external parameters(such as $\omega$) or internal parameters (such as $d$) are varied. We modelthis using the PP04 model of climate change. This is a forced discontinuousFilippov (non-smooth) dynamical system. When periodically forced this hasco-existing periodic orbits. We find that the transitions in this system aremainly due to grazing events, leading to grazing bifurcations. An analysis ofthe grazing bifurcations is given and the impact of these on the domains ofattraction and regions of existence of the periodic orbits is determined undervarious changes in the parameters of the system. Grazing transitions arise forgeneral variations in the parameters (both internal and external) of the PP04model. We find that the grazing transitions between the period orbits resemblethose of the Mid-Pleistocene-Transition.

Grazing bifurcations and transitions between periodic states of the PP04 model for the glacial cycle