I wondering what is the function of ferrite core in the induction cooker coil? (In the other word why there are no ferrite core in traditional induction heater?)
There are flux concentrators used in "traditional induction heaters." Flux concentrators are commonly used in heat treat applications, and are used on the back side of the coil like in your photograph.
The flux concentrator provides a low reluctance path for the magnetic field. This lowers the coil inductance, thus lowering the Q of the coil and load. The net effect is then a higher efficiency for heating.