Voice activated offline voice recorder
Audio Memos

This paid app lets you add a paid extension that allows you to have voice activated recording:


  
  Voice activated rec. - stop recording silence.
  


If you don't like IAPs, then you can download Audio Memos Pro from the same author (but it's more expensive than Audio Memos + IAP price.

Smart Recorder

This paid app also lets you have voice activated recording:


  
  Auto pause/voice activated recording