From Nookipedia, the Animal Crossing wiki
The Cyclommatus (ホソアカクワガタ, Hosoakakuwagata) is a stag-looking beetle with large mandibles, introduced in Animal Crossing: City Folk. They are found on palm trees and sell for 8,000 Bells. Compared to other stag beetles with a similar price, the Cyclommatus stag is less easily prone to scaring away; it does not react when villagers walk at full speed to it whereas the Elephant Beetle and Atlas Beetle will fly off. They are found between June and August, from 5 p.m. to 8 a.m..
Donating to the museum
In City Folk
"The calling card of the cyclommatus is its pair of mandibles, which are usually as long as its body. Another interesting fact is that the bug hates heat and will usually perish in a non-air-conditioned room. I can sympathize, eh wot? Leaving the sanctum of the museum for the summer heat is simply wretched."
After donation, the Cyclommatus can be found on the second tier of the insect section, in the large enclosure on the middle palm tree. This enclosure also contains the rafflesia, Tarantula, Scorpion, and Elephant Beetle, to name a few.
In New Leaf
After the donation, an information board will display a description of the Cyclommatus stag.
"Cyclommatus stags are identified by their long pairs of mandibles, which can be as long as their bodies. Their large mandibles are actually already formed when they're in the pupal stage of life. Although these beetles are mostly easygoing, those living in mountains really can't stand the heat."
Bug encyclopedia information
The first impression of the cyclommatus would be the large mandibles which measure up as long as the body, taking up half its full length. It uses these mandibles to fight off other beetles for a mate. The male cyclommatus is a lot larger than the female - the male being around 105mm and the female being 30mm.
Names in other languages