The　analytic　expressions　of　input-output　dynamic　parameters　of　memristor　(i.e.,　state　variable,　memristance,　and　output　response)　with　respect　to　initial　phase　of　sinusoidal　input　are　obtained　by　using　Homotopy　Analysis　Method　(HAM).　Furthermore,　a　new　exponent,　called　Response　Time　Delay　(difference)　between　the　Maximum　Values　of　input　and　output-RDMV-IO,　is　proposed　to　rapidly　analyze　the　memristor　input-output　dynamics,　under　different　initial　phases.　Employing　RDMV-IO,　we　further　reveal　the　intrinsic　relationship　between　initial　phase　and　dynamics.　The　studies　are　verified　by　using　Mathematica　simulations　adopting　nonlinear　dopant　drift　memristor　model　coupled　with　window　function.