Random walks arising from a Fibonacci's-rabbits scenario

摘要

1. Introduction At the beginning of the 13th century, Fibonacci posed a question concerning the potential growth of a rabbit population under ideal circumstances [1]. A version of this question is as follows: 'Suppose a newly-born pair of rabbits, one male, one female, are put in a field. Rabbits are able to mate at the age of one month, and have a gestation period of one month, so that at the end of her second month a female produces a pair of rabbits. Assuming that our rabbits never die, and that each female always produces exactly one mixed pair (one male, one female) from the end of her second month onwards, how many pairs will there be in one year?'