Abstract
A few models of nonlinear optical systems, known experimentally to possess both stable and unstable dynamical modes, are approximated by different dynamical models and integrated by different numerical methods. It is shown that the onset of instabilities and chaotic behavior in the same physical system may be dependent on the model used and on the numerical method applied. Finite order difference schemes should be applied with caution to infinite dimensional dynamical systems displaying irregular behavior.
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References
H.G. Schuster: Deterministic Chaos (Physikverlag, Weinheim 1988)
H. Bai-Lin: Elementary Symbolic Dynamics (World Scientific, Singapore 1989)
For an overview of numerical methods applicable to chaotic systems, see for example: T.S. Parker, L.O. Chua: Practical Numerical Algorithms for Chaotic Systems (Springer, New York 1989)
M. Yamaguti, S. Ushiki: Physica D 3, 618 (1981)
P. Günter, J.P. Huignard (eds.): Photorefractive Materials and Their Applications I and II, Topics Appl. Phys. Vol. 61 and Vol. 62 (Springer, Berlin, Heidelberg 1988, 1989)
K. Ikeda: Opt. Commun. 30, 257 (1979)
M. Lax et al.: J. Opt. Soc. Am. A 2, 731 (1985)
W. Krolikowski, M.R. Belić, M. Cronin-Golomb, A. Bledowski, J. Opt. Soc. Am. B 7, 1204 (1990)
N.V. Kukhtarev, V. Markov, S. Odulov: Opt. Commun. 23, 338 (1977)
M. Belić, D. Timotijevic, W. Krolikowski: J. Opt. Soc. Am. B 8, 1723 (1991)
“Discussion on the existence and uniqueness or multiplicity of solutions of the aerodynamical equations”, In: J. von Neumann Collected Works (Pergamon, Oxford 1961–1963) Vol. 6, p. 348
M. Sauer, F. Kaiser: Appl. Phys. B 55, 138–143 (1992)
L. Lugiato, R. Lefever: Phys. Rev. Lett. 58, 2209 (1987)
M. Le Berre, E. Ressayre, A. Tallet, H.M. Gibbs: Phys. Rev. Lett. 56, 274 (1986)
C. Grebogi, S.M. Hammel, J.A. Yorke, T. Sauer: Phys. Rev. Lett. 65, 1527 (1990)