the white zone need work like a magnet and if this magnet will be stop for 10 second i need to have the same warp effect on image for 10 second .. just like example..
The echo effect was just a quick suggestion but surely you can figure out a way to manipulate the gradient to get the effect you want and then use the displacement map on that gradient. Don't think you will find a plugin that works for this specific use case as it seems quite unusual.