- Author
- Simiu, E. | Frey, M. R. R. | Grigoriu, M.
- Title
- Necessary Condition for Homoclinic Chaos Induced by Additive Noise.
- Coporate
- National Institute of Standards and Technology, Gaithersburg, MD Cornell Univ., Ithaca, New York
- Sponsor
- Department of the Interior, Washington, DC
- Book or Conf
- Computational Stochastic Mechanics, Elsevier Applied Science, New York, Spanos, P. D.; Brebbia, C. A., Editors, 889-896 p., 1992
- Keywords
- noise (sound) | homoclinic orbit
- Abstract
- The effect of noise on the possible occurrence of chaos in systems with a homoclinic orbit was recently investigated in the literature on the basis of a redefinition of the Melnikov function. The purpose of this note is to show that, even in the case of deterministic equations, this redefinition is not consistent with the geometry of the perturbed orbits and would therefore lead to incorrect solutions. The possibility is then explored of developing a necessary condition for the occurrence of homoclinic chaos in forced systems perturbed additively by a commonly used approximate representation of white noise.