Bacterial　foraging　optimization　(BFO)　has　been　proved　to　be　an　efficient　optimization　method　and　successfully　applied　to　a　variety　of　fields　in　the　real　world.　In　BFO,　the　chemotaxis　process　is　a　complex　and　close　combination　of　swimming　and　tumbling　and　plays　a　crucial　role　in　searching　better　solutions.　A　previous　study　has　modeled　the　dynamics　of　the　chemotaxis　mechanism　mathematically　and　investigated　the　stability　and　convergence　behavior　of　the　chemotaxis　dynamics　over　the　one-dimensional　objective　function　by　Lyapunov　stability　theorem.　However,　this　study　appears　to　be　very　limited　from　a　practical　point　of　view,　and　how　to　extend　their　study　to　the　multi-dimensional　objective　function　is　a　challenge.　To　solve　it,　we　present　a　stability　analysis　of　chemotaxis　dynamics　in　BFO　over　the　multi-dimensional　objective　function　in　this　paper.　First,　the　general　mathematical　model　of　the　chemotaxis　mechanism　over　the　multi-dimensional　objective　function　is　created.　Secondly,　this　paper　uses　the　general　descent　search　to　analyze　the　general　mathematical　model　and　points　out　two　necessary　conditions　for　avoiding　the　bacterium　to　trap　into　a　non-optimal　solution.　And　then,　the　stability　and　convergence　of　the　chemotaxis　dynamics,　represented　by　the　general　mathematical　model,　are　proved　by　using　Lyapunov　stability　theorem.　Finally,　empirical　research　is　conducted　to　validate　the　above　theoretical　analysis.