Cannot sync my iPad with my iMac over USB - power problem

I want to sync my iPad (4th gen.) with my 27'' iMac using USB and iTunes. When I plug in the USB cable, it starts the device recognition but stops immediately as I could not confirm the connection in the iPad. The dialog is just popping up and disappears in the same second. Also the charging icon on the iPad ist flashing only. This looks to me as the iMac is not delivery enough power for a stable connection to the iPad. I only have attached a Logitech dongle for my wireless keyboard on another USB port. The rest is unused. We have tried different cables and even different iPads (2nd gen. also). Does anyone face the same issues and does anyone know a solution? OK buying or trying an USB hub could be a way, but I would be quite disappointed of my iMac if it cannot power two devices properly over USB. And to turn on WiFi sync I first need to have a connection between iMac and iPad.