A multi spool gas turbine engine with a differential having a selectively rotatable member which rotational speed determines a variable ratio between rotational speeds of driven and driving members of the differential. The driven member is engaged to the first spool and a rotatable shaft independent of the other spools (e.g. connected to a compressor rotor) is engaged to the driving member. First and second power transfer devices are engaged to the first spool and the selectively rotatable member, respectively. A circuit interconnects the power transfer devices and allows a power transfer therebetween, and a control unit controls the power being transferred between the power transfer devices. Power can thus be transferred between the first spool and the selectively rotatable member to change the speed ratio between the first spool and the rotatable shaft.