It is well known that different from most mammals with bihemispheric sleep, birds, some aquatic mammals, and reptiles engage in unihemispheric sleep to mitigate the fundamental conflict between sleep and wakefulness. The mechanism of this phenomenon has been illustrated by chimera states of coupled oscillators (Phys. Rev. Lett., 101 (2008) 084103) but its alternating character has not been studied so far. We here present a model to implement the alternating chimera states in two coupled groups of oscillators, which provides insight to understand the dynamic unihemispheric sleep. Moreover, we study the influence of distributed time delay and size asymmetry to the chimera states and find that the chimera states are robust to both the time delay distribution and the asymmetry of populations in the two coupled groups.

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