Collapsing effects in numerical simulation of chaotic dynamical systems

In control system design, whether the various subsystems are in discrete time or continuous time, the state space is usually regarded as a continuum. However, when the system is implemented, some subsystems may have a state space which is a subset of finite computer arithmetic. This is an important concern if a subsystem has chaotic behaviour, because it is theoretically possible for rich and varied motions in a continuum to collapse to trivial and degenerate behaviour in a finite and discrete state space [5]. This paper discusses new ways to describe these effects and reports on computer experiments which document and illustrate such collapsing behaviour.