Physics Letters A 303 (2002) 190–196 www.elsevier.com/locate/pla Robustness in the suppression of bidirectional chaotic escape from a potential well by weak parametric excitations R. Chacón a , F. Sánchez-Bajo a , J.A. Martínez b a Departamento de Electrónica e Ingeniería Electromecánica, Escuela de Ingenierías Industriales, Universidad de Extremadura, Apartado Postal 382, E-06071 Badajoz, Spain b Departamento de Ingeniería Eléctrica, Electrónica y Automática, Escuela Politécnica Superior, Universidad de Castilla-La Mancha, E-02071 Albacete, Spain Received 27 March 2002; received in revised form 2 July 2002; accepted 13 August 2002 Communicated by A.P. Fordy Abstract This Letter studies the robustness of the inhibition of bidirectional chaotic escape of a harmonically driven oscillator from a quartic potential well by the application of weak parametric excitations. We show that Melnikov-method-based theoretical predictions for harmonic escape-inducing excitations also work in the presence of external noise, and for chaotic-escape- inducing excitations having a sharp Fourier component with a sufficiently high power.  2002 Elsevier Science B.V. All rights reserved. PACS: 05.45.Gg; 05.40.Ca 1. Introduction Escape from a potential well is a very common phe- nomenon in science and engineering: the photodisso- ciation of molecules as described by the driven Morse oscillator [1], the stochastic escape of a trapped ion in- duced by a resonant laser field [2], and the capsizing of a boat subjected to trains of regular waves [3] are some illustrative examples. Fortunately, complex es- cape phenomena can often be well modeled by a low- dimensional system of differential equations. In par- ticular, many relevant properties of such phenomena have been characterized by means of a simple oscilla- E-mail address: rchacon@unex.es (R. Chacón). tor model with a quadratic nonlinearity: (1) ¨ x + x − x 2 =−η(x, ˙ x) + F cos(ωt), where −η(x, ˙ x) is a general dissipative force, and ω,F are the forcing frequency and amplitude, respec- tively. In such a case, escape is induced by a har- monic forcing, so that, before escape, transients of un- predictable duration—due to the fractal nature of the basin boundary—are usually observed [3–7]. On the other hand, chaotic escape is often undesirable tech- nologically, because erosion of the basin of attraction would limit the engineering integrity of large ampli- tude (periodic) states. In this regard, the application of weak, harmonic parametric excitations (PEs) to sys- tem (1) has been shown to be an effective procedure for inhibiting one-way chaotic escape [8,9]. However, 0375-9601/02/$ – see front matter  2002 Elsevier Science B.V. All rights reserved. PII:S0375-9601(02)01169-6