Publication Type:

Journal Article

Source:

International Journal of Bifurcation and Chaos, Volume 20, Number 3, p.697-702 (2010)

URL:

http://www.scopus.com/inward/record.url?eid=2-s2.0-77951904826&partnerID=40&md5=631919b04d1bf128623549114ae3f9a3

Keywords:

Analytic functions, Chaotic systems, Complex variable, Conservative systems, Cubic polynomials, Duffing equations, Hamiltonian systems, Hamiltonians, Lyapunov spectrum, Phase space methods, Phase space trajectory, Second orders, Space flight

Abstract:

It is shown that, for analytic functions f, systems of the form z̈=f(z*,ż) and z̈=f(z)cannot produce chaos; and that systems of the form z̈=f(z* , ż *) and z̈=f(z,z*) are conservative. Eight simple chaotic systems of the form z̈=f(z, z*) with quadratic and cubic polynomial f(z, z*) are given. Lyapunov spectra are calculated, and the systems' phase space trajectories are displayed. For each system, a Hamiltonian is given, if one exists. © World Scientific Publishing Company.

Notes:

cited By (since 1996)0

Cite this Research Publication

Da Marshall and Sprott, J. Cb, “Simple conservative, autonomous, second-order chaotic complex variable systems”, International Journal of Bifurcation and Chaos, vol. 20, pp. 697-702, 2010.