If someone has there defense Perplexed up by 2, do they still receive that +2 bonus to their defense if they are Pulse Waved?

Only of the characters with perplex are outside the pulsewave.

Depends.
If the Perplexer(s) are within range of the Pulse Wave attack, and the Pulse Waver's line of fire to them isn't blocked, then their Perplex is ignored, and the target doesn't get +2 to its defense value.
If the Perplexer(s) aren't within range of the Pulse Wave attack and/or the Pulse Waver's line of fire to them is blocked, then their Perplex isn't ignored, and the target does get the +2 to its defense value.

I though ignoring didn't equal countering.

Perplex isn't countered or lost when it's pulse waved.

It isn't countered, so the ongoing effect of it doesn't end. That said, if the Perplexer is in the PW radius, the Perplex IS ignored, so for that short time you treat the power as if it has no effect.

How does one know which powers to treat as if they have no effect for that short time and which powers continue to have an effect even when being ignored?

Any powers that are within range and line of fire (and line fire isn't blocked by pulsewave) of Pulsewave. This also goes for team abilities and theme probability. Basically, treat the dials and and bases as having no powers..just blank white dials/bases with numbers.

Just imagine Pulsewave as a giant nuclear bomb or explosion going off in a xx Radius. Is the invuln or prob control going to save you? Not a chance

What I'm talking about is the effects the powers have brought into play prior to the use of Pulse Wave.

We have some effects which aren't ignored because the power that caused them isn't being countered by Pulse Wave, e.g., Barrier, Super Strength.

And then, we have some effects which are ignored even though the power that caused them isn't being countered by Pulse Wave, e.g., Perplex.

What I want to know is, when it comes to other powers that might exist or will exist, how do I determine which effects are not ignored because the power isn't being countered, and which are ignored because the power is just being ignored.

Basically the players guide allows terrain features to stay because you need to counter the power in order to remove the terrain. Same with holding an object. Where Perplex if inside the Pulse Wave Range has its power ignored and since perplexed values don't come into effect cause of Replace then Modify they are floating numbers. If Perplex is ignored no floating numbers.

OK, I think I'm seeing why the modification from perplex would still be ignored.

So, the modifier wasn't actually increasing the defense of the character prior to when Pulse Wave was being used.

Thanks for your help