Chaotic behaviour in a bank account

Abstract

This paper presents a very simple one variable model, apparently not previously studied, of a bank account with no random elements yet which displays chaos. Interest is periodically added to the account and when the balance exceeds a pre-set limit then a fixed amount is removed into another account. The owner of the account is not required to make any additional deposits or withdrawals, nor is the rate of interest required to change for chaotic behaviour to be observed in the balance in the account. In the process of investigating this model we aim to introduce ideas from chaos theory to a wider audience. No previous knowledge of chaos theory or dynamical systems is assumed and all technical terms used from these areas are explained, these include: strange attractor, Lyapunov exponent, ergodicity, mixing, dense set, invariant set, measure zero, countable and uncountable infinities. The three defining properties of a chaotic system are presented and are shown to be possessed by the model.