Here are a few more phase plots of global temperature after the impulse of stratosphere-reaching eruptions, Mt Agung, Mt Chichon and Mt Pinatubo in 1963, 1982 and 1991 respectively. The impulses are cooling of course, due to the shielding of short-wave solar radiation by stratospheric aerosols. The tendency of the global temperature dynamic to oscillate around a mean is clear.
These patterns were then disrupted by large El Ninos.
The axes of the phase space are chosen to represent abstract position and momentum (in this case temperature and temperature changes). Position and momentum in a conserved system correspond to potential and kinetic energy. The appearance of a circle or a spiral is evidence of a system that conserves energy by transferring between potential (radiative imbalance in this case) and kinetic (mass transfer, convection?) so that the sum remains constant.