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In this paper we consider a system of identical three two-level atomsinteracting at resonance with a single-mode of the quantized field in alossless cavity. The initial cavity field is prepared in the coherent statewhile the atoms are taken initially to be either in the uppermost excited state"$|eee>$" or The $\textmd{GHZ}$-state or the $\textmd{W}$-state. For thissystem we investigate different kinds of atomic inversion and entanglement,which arise between the different parts of the system due to the interaction.Also the relationship, between entanglement and some other nonclassical effectsin the statistical properties, such as collapses and revivals in the atomicinversion where superharmonic effects appear, is discussed. The $Q$-functionsfor different cases are discussed. Most remarkably it is found that the$\textmd{GHZ}$-state is more robust against energy losses, showing almostcoherent trapping and Schr\"odinger-cat states can not be produced from suchstate. Also the entanglement of $\textmd{GHZ}$-state is more robust than the$\textmd{W}$-state. Another interesting feature found is that the state whichhas no pairwise entanglement initially will have a much improvement of suchpairwise entanglement through the evolution. Sudden death and sudden revival ofatoms-pairwise entanglement are produced with the $\textmd{W}$-state.

Some entanglement features of three-atoms Tavis-Cummings model: Cooperative case