Two of the dynamic characters are Jack Ryan and Marko Ramius.  Ryan is at first a quiet intelligence analyst, afraid of flying, and perfectly happy behind a desk or analyzing intelligence for his boss.  Throughout the course of the novel it becomes clear that he is also cool under pressure, brave, willing to take risks, and even reckless at times.  Ramius is difficult to pin down at first, alternating between a crazy old man and a brilliant man bent on revenge.  At the end he is perhaps some of both as well as a wise old seaman looking forward to a quiet life away from the drama of the story.

A static character would be the cook on the Red October, completely blind to any alternative to the Soviet ideal and willing to do anything to stop Ramius from successfully taking the Red October to the US and defecting.