Some simple chaotic jerk functions

One of the most remarkable recent developments in classical physics has been the realization that simple nonlinear deterministic equations can have unpredictable ~chaotic! long-term solutions. Chaos is now thought to be rather common in nature, and the study of nonlinear dynamics has brought new excitement to one of the oldest fields of science. The widespread availability of inexpensive personal computers has brought many new investigators to the subject, and important research problems are now readily accessible to undergraduates. An interesting and yet unsolved problem is to determine the minimum conditions necessary for chaos. This paper will describe several examples of chaotic flows that are algebraically simpler than any previously reported and will suggest further lines of promising investigation. The chaotic system to which one is usually first introduced is the logistic equation,