Generalization of the simplest autonomous chaotic system

An extensive numerical search of jerk systems of the form (chi) triple over dot + <(chi)double over dot> + chi = f(<(chi)single over dot>) revealed many cases with chaotic solutions in addition to the one with f ((x) over dot) = +/-(x) over dot(2) that has long been known. Particularly simple is the piecewise-linear case with f ((x) over dot)=alpha(1-(x) over dot) for (x) over dot >= 1 and zero otherwise, which produces chaos even in the limit of a co. 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. (C) 2011 Elsevier B.V. All rights reserved.