Wether or not it is an introduced species depends upon where he is.
West of the Rockies - it is introduced, and has wreaked havock - contributing to the extinction of the vegas valley leopard frog, and the endangered status of the California Red Legged frog.
But he may be in an area where they are native.
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With respect to declining populations being ecology "righting itself" - I find that highly unlikely.
Many creek systems where I use to catch bullfrogs are now completely void of them. They are completely void of any frogs - even the toads are gone. And the fish that use to be there are virtually gone as well.
Polution took its toll on those creek systems.
Furthermore - there is a worldwide amphibian decline.
Ecology does not "right itself" in the way you speak - it does not decide it doesn't want bullfrogs and then get rid of them to return to its previous state.
Ecology adapts to the presence of introduced species that are able to survive - and (unfortunately) that very often means the elimination of native species.