We investigate the entanglement dynamics of an anisotropic two-qubit Heisenberg XYZ system with Dzyaloshinskii-Moriya (DM) interaction in the presence of both inhomogeneity of the external magnetic field b and intrinsic decoherence which has been studied. The behavior of quantum correlation and the degree of entanglement between the two subsystems is quantified by using measurement-induced disturbance (MID), negativity (N) and Quantum Discord (QD), respectively. It is shown that in the presence of an inhomogeneity external magnetic field occur the phenomena of long-lived entanglement. It is found that the initial state is the essential role in the time evolution of the entanglement.
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