Abstract
In this lecture I would like to describe some recent ideas and techniques that I believe to be of great potential usefulness in studying a variety of nonlinear phenomena. The emphasis will be on bifurcation phenomena, since the properties of a nonlinear system can rarely be elucidated systematically at parameter values substantially far from their bifurcation values. I would also like to emphasize the usefulness of these techniques in studying systems described by partial differential equations. It is for this reason that I have chosen a specific fluid dynamical system to illustrate the ideas that I shall describe. Apart from my familiarity with doubly diffusive systems, I think it is generally helpful in this field to be as specific as possible.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
N.O. Weiss: Phil. Trans. Roy. Soc. A256, 99 (1964).
H.E. Huppert and J.S. Turner: J. Fluid Mech. 106, 299 (1981).
M.R.E. Proctor and N.O. Weiss: Rep. Prog. Phys. 45, 1317 (1982).
E. Knobloch: Phys. Fluids 23, 1918 (1980).
J. Marsden and M. McCracken: The Hopf Bifurcation and Its Applications, Springer Verlag (1976).
P.G. Daniels: Proc. Roy. Soc. A358, 173 (1977).
P. Hall and I.C. Walton: Proc. Roy. Soc. A358. 199 (1977).
L.N. Da Costa, E. Knobloch and N.O. Weiss: J. Fluid Mech. 109, 25 (1981).
J. Guckenheimer and E. Knobloch: Geophys. Astrophys. Fluid Dyn. 23, 247 (1983).
J. Guckenheimer and P. Holmes: Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, Springer Verlag (1983).
V.I. Arnol’d: Functional Anal, and Applics. 11, 85 (1977).
E. Knobloch and M.R.E. Proctor: J. Fluid Mech. 108, 291 (1981).
J. Guckenheimer and E. Knobloch, in preparation.
D. Moore, J. Toomre, E. Knobloch and N.O. Weiss: Nature 303, 663 (1983).
E. Knobloch, D. Moore, J. Toonre and N.O. Weiss, in preparation.
E. Knobloch and N.O. Weiss: Phys. Lett. 85A, 127 (1981).
E. Knobloch and N.O. Weiss: Physica D, in press.
L.P. Shil’nikov: Soviet Math. Doklady 6, 163(1965).
J. Yorke and K. Alligood: Bull. Amer. Math. Soc., in press.
P. Glendinning and C. Sparrow: preprint.
E. Buzano and M. Golubitsky: Phil. Trans. Roy. Soc. A308, 617(1983).
M. Golubitsky, J.W. Swift and E. Knobloch: Physica D, in press.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1984 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Knobloch, E. (1984). Bifurcations in Doubly Diffusive Convection. In: Kuramoto, Y. (eds) Chaos and Statistical Methods. Springer Series in Synergetics, vol 24. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-69559-9_20
Download citation
DOI: https://doi.org/10.1007/978-3-642-69559-9_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-69561-2
Online ISBN: 978-3-642-69559-9
eBook Packages: Springer Book Archive