Questions about movement of a permanent magnet inside of solenoid.

I have been doing some experimenting with a relatively short cylindrical permanent magnet and a solenoid with DC current applied. I would like an explanation as to why these two things happen. The OD of the cylindrical magnet is just a little bit smaller then the ID of the solenoid.

Placing the magnet near the left end of the solenoid and applying current will cause the magnet to move to the right and stop at the center of the solenoid. Manually moving the magnet back slightly to the left and reversing current will cause the magnet to move to the left.

Placing the magnet near the left end of the solenoid and applying current will cause the magnet to move to the right and stop at the center of the solenoid. Manually moving the magnet slightly to the right and reversing current will cause the magnet to continue moving to the right.

Before doing these experiments my conjecture was that the magnet placed at the end of the solenoid would pass completely through the solenoid. My thinking was that movement of the magnet would be caused by the flux lines of the magnet and the solenoid being in different directions all the way through the inside of the solenoid.

My next though is that the flux lines moving through the center of the solenoid in the opposite direction as the magnets flux lines bulge out around the magnet kind of like a snake swallowing something. Somehow the magnet finds equilibrium in the center of the solenoid.
I have been watching the MIT open course physics lectures http://openlearning.wordpress.com/2007/12/19/the-walter-lewin-lectures and understand some of the concepts but still don't know how to apply them to this situation.

Any help would be greatly appreciated. Thank you.