Publication Type:

Journal Article

Source:

Chaos, Volume 19, Number 1 (2009)

URL:

http://www.scopus.com/inward/record.url?eid=2-s2.0-63849227475&partnerID=40&md5=198bad3db28c8b88b74db6a5544db76c

Abstract:

Despite a search, no chaotic driven complex-variable oscillators of the form z +f (z) = eit or z +f (z-) = eit are found, where f is a polynomial with real coefficients. It is shown that, for analytic functions f (z), driven complex-variable oscillators of the form z +f (z) = eit cannot have chaotic solutions. Seven simple driven chaotic oscillators of the form z +f (z, z-) = eit with polynomial f (z, z-) are given. Their chaotic attractors are displayed, and Lyapunov spectra are calculated. Attractors for two of the cases have symmetry across the x=-y line. The systems' behavior with as a control parameter in the range of =0.1-2.0 is examined, revealing cases of period doubling, intermittency, chaotic transients, and period adding as routes to chaos. Numerous cases of coexisting attractors are also observed. © 2009 American Institute of Physics.

Notes:

cited By (since 1996)4

Cite this Research Publication

Da Marshall and Sprott, J. Cb, “Simple driven chaotic oscillators with complex variables”, Chaos, vol. 19, 2009.