This is a picture of large brown butterfly with eyespots, called the Northern Pearly Eye. It is found in Michigan and other Great Lake states in the summer months. It is rather hard to tell apart from other little brown butterflies with eyespots, so consult a book, such as Butterflies of the Northwoods.
Book Review: Butterflies of the North Woods
Butterflies of the North Woods by Larry Weber is an excellent field guide for identification of butterflies. It is part of the North Woods Naturalist series, covering the states of Minnesota, Wisconsin, Michigan, and Ontario, Canada. How many times have you seen a butterfly flying by, and weren’t sure what it was? This field guide not only has excellent photos, but it also has a lot of information on the habits of butterflies, such as what food they eat and what food the butterfly caterpillars eat. It really helped me out, because we get a lot of brown butterflies with eyespots in this area that all look very similar. It helped me to differentiate between them, by comparing the number of eyespots, etc. Also included is an interesting section on the history of butterflies, such as: butterflies are really a type of moth that may have started flying during the day to get away from moth-eating bats. There is also information on day-flying moths that only look like butterflies. Also part of the series: Moths and Caterpillars of the North Woods, Dragonfies of the North Woods, and Damselflies of the North Woods.
Reference: Larry Weber, Butterflies of the North Woods, 2nd edition,(Duluth,MN:Kollath+Stensaas Publishing, 2006)