Convergence, oscillations, and chaos in a discrete model of combat

A piecewise smooth mapping of the three-dimensional Euclidean space is derived from a discrete-time model of combat. The mathematical analysis of this mapping focuses on the effects of discontinuity caused by the defender's withdrawal strategy – a prime component of the original model. Both the asymptotics and the transient behavior are discussed, and all the behavior types noted in the title are established as possible outcomes.