The periodic changes of atmospheric CO2 and temperature over the last 5 Myr reveal three features that challenge current climate research, namely: (i) the mid-Pleistocene transition of dominant 41-kyr cycles to dominant 100-kyr cycles, (ii) the absence of a strong precession signal of approximately 20 kyr, and (iii) the cooling through the middle and late Holocene. These features are not directly addressable by Earth's orbital changes described by Milankovitch. Here we show that a closed photochemical system exposed to a constant illumination source can sustain oscillations. In this simple conceptual model, the oscillations are intrinsic to the system and occur even in the absence of periodic radiative forcing. With proper adaptations to the Earth system, this oscillator explains the main features of past climate dynamics. Our model places photosynthesis and the carbon cycle as key drivers of climate change. We use this model to predict the relaxation of a 1,000 PgC pulse of CO2. The removal of 50% of this CO2 will require one century, and will lead to a warmer and wetter future. However, more pronounced glaciation cycles emerge on the millennial timescale.