Eur. Phys. J. B 30, 207-210 (2002)
https://doi.org/10.1140/epjb/e2002-00375-6

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 rchacon@unex.es

Received: 21 May 2002
Revised: 13 September 2002
Published online: 29 November 2002

Abstract

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.