A stochastic digital oscillating system induced by the truncation error

Abstract

It is generally believed that chaotic systems will collapse due to computer truncation error. In this paper we introduce a contrary example, in which a simple system is induced to complication or chaos completely by computer truncation. The system is defined as a cross-focus system in elliptical reflecting cavity map system. The theoretical solution is a limiting sequence and the computer solution is a stochastic digital oscillating system induced from the theoretical solution by truncation error. There is only a turn-round mechanism in the system theoretically. On the other hand, round-off induces the nonhyperbolic fixed points in the system to produce a new escape mechanism of intermittent chaos.