Audio　bandwidth　extension　can　artificially　restore　the　truncated　high　frequencies　at　the　decoder　from　the　transmitted　low-frequency　signal.　This　paper　presents　a　new　method　for　blind　bandwidth　extension　of　wideband　audio　based　on　harmonic　mapping　in　phase　space.　First,　the　spectral　series　of　audio　signal　is　represented　by　using　phase　space　reconstruction.　Then,　the　harmonics　of　high　frequencies　are　mapped　out　from　the　evolutionary　trajectories　of　low-frequency　components　in　phase　space　by　using　nonlinear　prediction.　Combining　with　spectral　envelope　estimation　of　high　frequencies　based　on　Gaussian　mixture　model,　the　bandwidth　of　wideband　audio　signals　can　be　effectively　extended　to　super　wideband,　without　any　side　information.　Subjective　and　objective　testing　results　indicate　that　the　proposed　method　improves　the　harmonic　characteristics　of　the　extended　super-wideband　audio　and　achieves　a　better　quality　than　conventional　blind　bandwidth　extension　methods.