Relative effectiveness of weak periodic excitations in suppressing homoclinic/heteroclinic chaos
Departamento de Electrónica e Ingeniería Electromecánica, Escuela de Ingenierías Industriales, Universidad de Extremadura, 06071 Badajoz, Spain
Corresponding author: a firstname.lastname@example.org
Revised: 13 September 2002
Published online: 29 November 2002
Melnikov-method-based theoretical results are demonstrated concerning the relative effectiveness of any two weak excitations in suppressing homoclinic/heteroclinic chaos of a relevant class of dissipative, low-dimensional and non-autonomous systems for the main resonance between the chaos-inducing and chaos-suppressing excitations. General analytical expressions are derived from the analysis of generic Melnikov functions providing the boundaries of the regions as well as the enclosed area in the amplitude/initial phase plane of the chaos-suppressing excitation where homoclinic/heteroclinic chaos is inhibited. The relevance of the theoretical results on chaotic attractor elimination is confirmed by means of Lyapunov exponent calculations for a two-well Duffing oscillator.
PACS: 05.45.Ac – Low-dimensional chaos / 05.45.Pq – Numerical simulations of chaotic models / 05.45.Gg – Control of chaos, applications of chaos
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2002