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Recent observations show that our universe is accelerating by dark energy, soit is important to investigate the thermodynamical properties of it. TheUndulant  Universe is a model with equation of state $\omega(a)=-\cos(b\ln a)$ for darkenergy, where we show that there neither the event horizon nor the particlehorizon exists. However, as a boundary of keeping thermodynamical properties,the apparent horizon is a good holographic screen. The Universe has a thermalequilibrium inside the apparent horizon, so the Unified First Law and theGeneralized Second Law of thermodynamics are satisfied. As a thermodynamicalwhole, the evolution of the Undulant Universe behaves very well in the currentphase. However, when considering the unification theory, the failure ofconversation law at the epoch of the matter dominated or near singularity needsome more consideration for the form of the Undulant Universe.

Thermodynamical properties of the Undulant Universe