PapersNo Access

STABILITY OF STEADY-STATE SOLUTIONS IN MULTIDIMENSIONAL COUPLED MAP LATTICES

MIROSLAVA DUBCOVÁ

Department of Mathematics, Institute of Chemical Technology, Prague, Czech Republic

Search for more papers by this author

DANIEL TURZÍK

Department of Mathematics, Institute of Chemical Technology, Prague, Czech Republic

Search for more papers by this author

, and

ALOIS KLÍČ

Department of Mathematics, Institute of Chemical Technology, Prague, Czech Republic

Search for more papers by this author

https://doi.org/10.1142/S0218127404011107Cited by:0 (Source: Crossref)

Abstract

Coupled map lattices with multidimensional lattice are considered. A method for the determination of the stability of spatially homogeneous and spatially periodic steady-state solutions is derived. This method is based on the determination of the spectrum of the linearized operator by means of Gelfand transformation of some appropriate Banach algebra. The results are applied to several examples.

Keywords:

References

V. S. Afraimovich and L. A. Bunimovich, Rand. Comput. Dyn. 1, 423 (1992). Google Scholar
V. S. Afraimovich, L. Y. Glebsky and V. I. Nekorkin, Rand. Comput. Dyn. 2, 287 (1994). Google Scholar
V. S. Afraimovich and L. A. Bunimovich, Physica D80, 277 (1995). Google Scholar
B. Aupetit , A Primer on Spectral Theory ( Springer-Verlag , NY , 1991 ) . Crossref, Google Scholar
L. A. Bunimovich and Ya. G. Sinai, Nonlinearity 1, 491 (1988). Crossref, Web of Science, Google Scholar
L. A. Bunimovich and E. A. Carlen, J. Diff. Eqs. 123, 213 (1995). Crossref, Web of Science, Google Scholar
M. Dubcováet al., Int. J. Bifurcation and Chaos 13, 343 (2003). Link, Web of Science, Google Scholar
R. Harte, Proc. Roy. Irish Acad. A88, 103 (1988). Google Scholar
K. Kaneko (ed.) , Theory and Applications of Coupled Map Lattices ( Chichester, NY , 1993 ) . Google Scholar
D. Turzíket al., Dyn. Syst.: An Int. J. 18, 23 (2002). Crossref, Web of Science, Google Scholar