Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-22T04:45:39.030Z Has data issue: false hasContentIssue false
  • English
  • Français

Aspects of laser Lorenz dynamics

Published online by Cambridge University Press:  17 February 2009

P. B. Chapman
P. B. Chapman
Affiliation:
Department of Mathematics, University of Western Australia, Nedlands, W.A., 6009
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The laser Lorenz equations are studied by reducing them to a form suitable for application of an extension of a method developed by Kuzmak. The method generates a flow in a Poincaré section from which it is inferred that a certain Hopf bifurcation is always subcritical.

Type
Research Article
Information
The ANZIAM Journal , Volume 36 , Issue 2 , October 1994 , pp. 152 - 174
Copyright
Copyright © Australian Mathematical Society 1994

References

[1]Bourland, F. J. and Haberman, R., “Separatrix crossing: time invariant potentials with dissipation”, SIAM J. Appl. Math. 50 (1990) 1716–1744.CrossRefGoogle Scholar
[2]Coddington, E. A. and Levinson, E., Theory of ordinary differential equations (McGraw-Hill, New York, 1955).Google Scholar
[3]Flessas, G. P., “New exact solutions of the complex Lorenz equations”, J. Phys. A: Math. Gen. 22 (1989) L137–L141.CrossRefGoogle Scholar
[4]Fowler, A. C., Gibbon, J. D. and McGuinness, M. J., “The complex Lorenz equations”, Physica D 4 (1982) 139–159.CrossRefGoogle Scholar
[5]Fowler, A. C. and McGuinness, M. J., “On the nature of the torus in the complex Lorenz equations”, SIAM J. Appl. Math. 44 (1984) 681–700.CrossRefGoogle Scholar
[6]Jeffreys, H. and Jeffreys, B. S., Methods of mathematical physics, third ed. (Cambridge University Press, Cambridge, 1956).Google Scholar
[7]Kuzmak, G. E., “Asymptotic solutions of second order differential equations with variable coefficients”, J. Appl. Math. Mech. 23 (1959) 730–744.CrossRefGoogle Scholar
[8]Weiss, C. O. and Vilaseca, R., The dynamics of lasers (VCH, Weinheim, 1991).Google Scholar
[9]Zeghlache, H., Mandel, P., Abraham, N. B. and Weiss, C. O., “Phase amplitude dynamics of the laser Lorenz model”, Phys. Rev. A 38 (1988) 3128–3131.CrossRefGoogle ScholarPubMed