I understand that you can use a gyrator to simulate capacitors or inductors with (very) high values. A capacitor stores its energy in an electric field, an inductor in a magnetic field. Where is the (high?) energy of a simulated 10H inductor? The gyrator doesn't even have to have an inductor. This gyrator simulates an inductor of 1H for every 2\$\mu\$F.
The gyrator simulates only some of the properties of the inductor, e.g. its frequency characteristics and Q factor, but not all of them, e.g. not energy storage.
This Wikipedia article explains that a 'true' gyrator is a hypothetical component, and that some circuits (like the one you've drawn) can be used to simulate some of how an inductor behaves using capacitors and active compoments like opamps.
