Is it possible to pulse on a LED strip as the warp engines do on Star Trek TNG?
The easiest way to do this sort of thing is a microcontroller with a PWM (Pulse Width Modulation) output.  Feed the output pin to a MOSFET, which drives the LEDs.  There are plenty of examples on the web.
For a hobbyist, an Adruino would do it.  For something more compact and lower power, almost any small microcontroller would do.  Being programmable, you can make it do any flashing pattern you want.