Abstract
An extensive numerical search of jerk systems of the form x⃛+x¨+x=f(x˙) revealed many cases with chaotic solutions in addition to the one with f(x˙)=±x˙2 that has long been known. Particularly simple is the piecewise-linear case with f(x˙)=α(1−x˙) for x˙⩾1 and zero otherwise, which produces chaos even in the limit of α→∞. The dynamics in this limit can be calculated exactly, leading to a two-dimensional map. Such a nonlinearity suggests an elegant electronic circuit implementation using a single diode.
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