In this paper, we analytically explore the dynamics of a nonlinear two-qubit system derived from a phys- ical model that describes laser-irradiated two trapped particles in the Lamb-Dicke regime under appro- priate resonance conditions and the intrinsic decoherence. The dynamics of the particle population in- version, the entanglement between the two trapped-particles and their center-of-mass modes, and the entanglement between the two trapped-particles are investigated under the Lamb-Dicke parameter and the intrinsic decoherence. In is found that, in the absence of decoherence, the generated particle-field and two trapped-particles entanglement can be enhanced by increasing the Lamb-Dicke parameter. The Lamb-Dicke nonlinearity effect on the generated stationary entanglement, the sudden death and sudden birth of the entanglement, and the intrinsic decoherence effect become more pronounced with its large values. For the high Lamb-Dicke non-linearity, the decoherence effect on the generated nonclassical ef- fects can be weakened.