going interest in the genuine multipartite entanglement (GME) of the Dicke states for multiple qubits systems [novo,horodecki]{}. Most of the existing studies of entanglement focus on bipartite entanglement in the reduced state of two parties of a multipartite system [nielsen,roscilde,giamp,zurek]{}, which can be quantified through the von Neumann entropy [@wehrl; @schu] and the concurrence characterizing qubit-qubit entanglement [@wang; @vidal; @zhang1]. However, bipartite entanglement can only give a partial characterization. Multipartite entanglement is known to be different from entanglement between all bipartitions [ali,Guhne,bodoky]{}. Recently the bipartite entanglement decoherence has been studied in connection with a phenomenon termed entanglement sudden death, indicating that the bipartite entanglement can decay to zero abruptly during a finite period of time [yu1]{}. Whether this property occurs for the dynamics of GME remains unexplored. So it is highly desirable to study both the bipartite entanglement and the GME for the multipartite entanglement in the more than two qubits system, where the three qubits and cavity coupling system can be served as the most simple paradigm.

The paper is outlined as follows. In Sec. II, we map the three-qubit Dicke model with the CRW interactions into a solvable Hamiltonian by the zeroth- and first-order approximation, giving an analytical 