Determining nonchaotic parameter regions in some simple chaotic jerk functions

In this paper we apply Theorem 2.1 in [Heidel J, Zhang F. Nonchaotic and chaotic behaviour in the three-dimensional quadratic systems: five-one conservative cases, in press] to some simple chaotic jerk functions listed in [Sprott JC. Simple chaotic systems and circuits. Am J Phys 2000;68(8):758–63; Sprott JC. Algebraically simple chaotic flows. Int J Chaos Theory Appl 2000;5(2):1–20] to locate the parameter regions at which they are nonchaotic. We show that for each of the twenty chaotic systems studied here there are some nonchaotic parameter regions. This indicates that our theorem will help reduce the amount of work searching for parameters causing chaos. We also generalize Theorem 2.1 to include systems with exponential functions.