The　bursting　oscillation　is　a　fast-slow　oscillation.　A　complex　four-dimensional　coupled　Mathieu-van　der　Pol　oscillator　is　analyzed　to　investigate　the　bursting　oscillations.　The　multiscale　phenomena　appear　in　four-dimensional　coupled　Mathieu-van　der　Pol　oscillator　due　to　the　significant　difference　between　the　natural　frequencies　of　the　system　and　frequencies　of　the　parametric　excitation.　Analyzing　the　bifurcation　diagrams　of　four-dimensional　coupled　Mathieu-van　der　Pol　oscillator　using　the　bifurcation　theory　and　fast-slow　analysis,　we　identify　four　different　bursting　oscillation　modes.　Additionally,　an　intriguing　phenomenon　is　observed　as　the　parameters　of　the　fast　and　slow　systems　change　in　the　orbits.　This　phenomenon　is　called　as　the　slow　channel　effect.　The　trajectory　traverses　the　bifurcation　point　without　the　immediate　bifurcation　behaviors　but　gradually　converges　to　a　stable　limit　cycle　after　an　apparent　delay.　Four-dimensional　coupled　Mathieu-van　der　Pol　oscillator　has　a　composite　Hopf　bifurcation　which　means　that　a　Hopf　bifurcation　respectively　corresponds　to　the　large　and　small　limit　cycles.　This　research　provides　the　insights　into　the　mechanism　of　the　bursting　oscillations.　©　2023