Abstract
We study the nonlinear resonant coupling of two waves in a plasma for strong dissipation. We show that the corresponding system of differential equations has a saddle-focus fixed point and study its stable and unstable manifolds. The results we obtain suggest that the stochasticity which is numerically observed might be due to the existence of a spiral-type strange attractor.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
P. Terry and W. Horton,Phys. Fluids 25:3 (1982).
S. Vyshkind and M. Rabinovich,Sov. Phys. J.E.T.P. 44:292, 1976.
G. Laval and R. Pellat, inPlasma Physics, Les Houches, (Gordon and Breach, New York, 1972).
C. Meunier, M. N. Bussac, and G. Laval,Physica D:236–243 (1982).
M. N. Bussac,Phys. Rev. Lett. 49(26), (1982).
L. P. Shilnikov,Sov. Math. Dokl. 6:163–166 (1965).
L. P. Shilnikov,Math. U.S.S.R. Sbornik 10:91–102 (1970).
C. Tresser,Ann. Inst. Henri Poincaré Phys. Théor. 41(1), (1984).
A. Arneodo, P. Coulet, and C. Tresser,Commun. Math. Phys. 79:573 (1981).
E. Coddington and N. Levinson,Theory of Ordinary Differential Equations (McGraw-Hill, New York, 1955).
A. Kelley, inTransversal Mappings and Flows, R. Abraham and J. Robbin, eds. (Benjamin, New York, 1967).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Meunier, C. Nonlinear coupling of waves in a plasma in a strong dissipation limit. J Stat Phys 40, 759–782 (1985). https://doi.org/10.1007/BF01009899
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01009899