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　RDMVIO,　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.　©　2019　The　Institute　of　Electronics,　Information　and　Communication　Engineers.