A Simple Chaotic Flow with a Continuously Adjustable Attractor Dimension

作者：Munmuangsaen Buncha^*; Sprott Julien Clinton; Thio Wesley Joo Chen; Buscarino Arturo; Fortuna Luigi

来源：International Journal of Bifurcation and Chaos, 2015, 25(12): 1530036.

DOI：10.1142/S0218127415300360

• Chaos
• dynamical system
• differential equation
• conservative system
• low-dimensional chaos

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.

• 出版日期2015-11