MELNIKOV FUNCTION AND HOMOCLINIC CHAOS INDUCED BY WEAK PERTURBATIONS - REPLY

For the case of weak perturbations, our theory is shown to reproduce e xactly the results of Simiu and Frey [Phys. Rev. E 48, 3185 (1993)]. I n the presence of weak noise, the two approaches yield different resul ts. This can be traced to the neglect of diffusion effects in the Simi u-Frey theory; the inclusion of these effects, via an ensemble-average d redefinition of the Melnikov function, leads to an additional term i nvolving the noise variance.