This　paper　investigates　a　locally　coupled　neural　oscillator　autonomous　system　qualitatively.　By　applying　an　approximation　method,　we　give　a　set　of　parameter　values　with　which　an　asymptotically　stable　limit　cycle　exists,　and　the　sufficient　conditions　on　the　coupling　parameters　that　guarantee　asymptotically　global　synchronization　are　established　under　the　same　external　input.　A　gradational　classifier　is　introduced　to　detect　synchronization,　and　the　network　model　based　on　the　analytical　results　is　applied　to　image　segmentation.　The　performance　is　comparable　to　the　results　from　other　segmentation　methods.