This paper describes two simple three-dimensional autonomous chaotic flows whose attractor dimensions can be adjusted continuously from 2.0 to 3.0 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.

A Simple Chaotic Flow with a Continuously Adjustable Attractor Dimension

BUSCARINO, Arturo;FORTUNA, Luigi
2015

Abstract

This paper describes two simple three-dimensional autonomous chaotic flows whose attractor dimensions can be adjusted continuously from 2.0 to 3.0 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.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11769/17753
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