Publication Type:

Journal Article


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



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


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.


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.