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We study the entanglement dynamics of the system comprising three two-level atoms resonantly interacting with three coupled cavities which are in weak coherent states initially. The atom-atom entanglement and cavity-cavity entanglement are investigated. The influences of coupling constant between cavities and intensity of the cavity field on entanglement properties are discussed. The results obtained using the numerical method show that atom-atom entanglement and cavity-cavity entanglement are both strengthened with the increase of intensity of the cavity field; on the other hand, atom-atom entanglement is weakened and the entanglement between cavity A and cavity B is strengthened with the increase of the coupling constant between cavities, and the entanglement between cavity B and cavity C has a nonlinear relation with the increase of the cavity-cavity coupling coefficient. These results are different from those in the case that cavity field is in vacuum state initially.
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