Vortex-induced　vibrations　(VIVs)　of　a　fixed　two-dimensional　perimeter-reinforced　(PR)　membrane　wing　at　Re　(Reynolds　number)　1000　and　(angle　of　attack)　30　are　investigated　using　fluid-structure　interaction　simulations.　By　employing　very　fine　increments　for　Re　and　,　bifurcation　boundaries　of　the　dynamic　response　of　the　membrane　wing　in　the　Re-　plane　are　captured.　With　increase　in　Re　and/or　,　it　is　found　that　the　VIV　state　of　a　fixed　PR　membrane　wing　will　change　progressively　from　static　state　to　period　1　via　a　Hopf　bifurcation　and　then　from　period　1　to　multiple　period　and　chaos　via　a　succession　of　period-doubling　bifurcations.　The　Hopf　bifurcation　is　triggered　by　the　shedding　of　the　leading-　and/or　trailing-edge　vortices,　while　the　period-doubling　bifurcations　are　induced　by　the　appearance　and　evolution　of　the　secondary　vortices　on　the　upper　surface　of　the　membrane　wing　at　higher　Re　and　.　With　an　increase　in　the　structure　rigidity　or　pre-strain,　the　overall　responses　of　the　membrane　wing　are　not　changed　much　in　the　Re-　plane　except　that　the　period　1　response　near　and　is　destroyed,　due　to　the　significant　change　of　the　shedding　process　of　the　leading-edge　vortices.　Moreover,　it　is　also　found　that　unsteady　responses　of　the　PR　membrane　wing　at　can　be　suppressed　by　small　pre-strain.