E. Simiu et M. Frey, MELNIKOV FUNCTION AND HOMOCLINIC CHAOS INDUCED BY WEAK PERTURBATIONS - COMMENT, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 48(4), 1993, pp. 3190-3192
The effect of noise on the possible occurrence of chaos in systems wit
h a homoclinic orbit (e.g., the Duffing equation) was recently conside
red by Bulsara, Schieve, and Jacobs [Phys. Rev. A 41, 668 (1990)], and
Schieve and Bulsara [Phys. Rev. A 41, 1172 (1990)], who adopted an ap
proach based on a redefinition of the Melnikov function. We show that
this redefinition is unsatisfactory and leads to incorrect results.