A Simple Chaotic Flow with a Continuously Adjustable Attractor Dimension

Abstract

This paper describes two simple three-dimensional autonomous chaotic flows whose attractor dimensions can be adjusted continuously from [Formula: see text] to [Formula: see text] by a single control parameter. Such a parameter provides a means to explore the route through limit cycles, period-doubling, dissipative chaos, and eventually conservative chaos. With an absolute-value nonlinearity and certain choices of parameters, the systems have a vast and smooth continual transition path from dissipative chaos to conservative chaos. One system is analyzed in detail by means of the largest Lyapunov exponent, Kaplan–Yorke dimension, bifurcations, coexisting attractors and eigenvalues of the Jacobian matrix. An electronic version of the system has been constructed and shown to perform in accordance with expectations.