In　this　paper,　we　study　the　dynamics　of　a　two-dimensional　coupled　cavity　system　under　one-excitation　condition.　We　show　that　the　dynamics　behaviors　are　strongly　affected　by　the　atom-cavity　detuning　(Δ)　and　cavity-cavity　hopping　υ.　As　a　typical　application,　we　apply　this　system　to　generate　a　four-atom　W　state.　Notably,　the　entangled　state　generation　is　deterministic.　As　a　basic　research,　the　result　will　contribute　to　the　understanding　of　more　complex　systems.　©　2015,　Springer　Science+Business　Media　New　York.