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.
cited By (since 1996)4
Da Marshall and Sprott, J. Cb, “Simple driven chaotic oscillators with complex variables”, Chaos, vol. 19, 2009.