Irruptions and crash of ungulate populations occur globally. A sika deer (Cervus nippon) population on Nakanoshima Island (southwestern Hokkaido, Japan) is one of the few whose long-term trends have been studied over two cycles of irruption and crash. Population crash was found to be associated with food shortages. After the first crash in 1984, deer shifted to new food items, including unpalatable plants that were not previously eaten by these animals. When quantities of unpalatable plants exceeded the quantities of palatable plants, the deer population increased again at a reduced rate but reached a larger population size than after the first irruption. Deer depends on fallen leaves after the second crash. To investigate the process, we constructed a mathematical model of deer and food plant population dynamics. Mathematical analysis and computer simulations quantitatively explained deer population dynamics when the animal population increased until the food is exhausted, when animals shift to new food at a low rate and when this new foraging behavior continues in the next generation. We investigate effects of shift rate between deer types on the population dynamics. If the shift rate or the population size was sufficiently large, these crash did not repeat. It suggests that repeated crash will occur in small habitats.