there is an effect called compound blur that allows you to control the amount of blur with the luminance of another layer (like a gradient layer).m apply the effect to the layer that you want to blur, then select the gradient layer as the layer map, adjust the blur from there.
if you use a shape layer with a gradient fill, you won’t need to pre-comp the gradient layer. if you use a solid with the gradient effect, or gradient layer style, you’ll need to precept the layer before you can use it as a layer map in compound blur.
however, as dave points out, your example has more of a chromatic aberration effect. if you search the web for that you should be able to find tutorials on creating that look. they usually involve separating our animation into red, blue and green channels, distorting each slightly (like with the bulge effect) and then recombining them in to the final RGB image.
Kevin Camp
Art Director
KCPQ, KZJO & KRCW