Advantages of using active inductors in ICs
The name gyrator is just a convenient term for an electronic circuit that replaces the functionality of a grounded inductor. There may be circuits called gyrators that can replace the functionality of a series inductor but these are much rarer and are probably explained away using conventional filter explanations anyway.


  Which is a typical value?


But, if you want a really common example of a circuit that somewhat mimics an inductor, try thinking about a constant current source or sink. It mimics an inductor value of infinite henries and they are used all over the place, inside and outside analogue chips.