Abstract
As far as pattern formation, front propagation and phase dynamics are concerned, a lot has been achieved in various, yet related, specific fields. Let us mention just some of these: in hydrodynamics, the equations of the Rayleigh-Benard convection by Newell & Whitehead [1] and the instability of convective flows [2], the phase instability of oscillating systems by Kuramoto [3], the propagation of fronts in combustion by Sivashinski [4], the Eckhaus instability of steady structures [5], the topological turbulence in the Ginzburg-Landau equation [6]. Finally, to return to topics more directly related to this work, and with no pretention to exhaustivity, we should cite the works of Winfree [7], Tyson [8], Fife [9], Keener [10], Mikhailov & Krinskii [11] Meron & Pelce [12]. These mostly deal with theory. Of course, much has been done in experiments, which we should only cite indirectly, through review articles or collective works [13, 14, 15].
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
Newell, A.C. & Whitehead, J.C. (1969). J. Fluid Mech. 38, 279.
Pomeau, Y. & Manneville, P. (1979). J. Phys. Lett. 40, L610.
Kuramoto, Y. (1984). Chemical Oscillations, Waves and Turbulence. Springer.
Sivashinski, G.I. (1977). Acta Astron. 4, 1177.
Eckhaus, W. (1965). Studies in Nonlinear Stability Theory. Springer.
Coullet, P., Gil, L. & Lega, J. (1989). Phys. Rev. Lett. 62(14), 1619.
Winfree, A.T. (1980). The geometry of biological time. Springer.
Tyson, J. (1987). J. Chim. Phys. 84, 1359–1365.
Fife, P.C. (1984). In Non-equilibrium Dynamics in Chemical systems, Vidal, C. & Pacault, A. (eds.), pp. 76–88. Springer.
Keener, J. (1989). Physica D34, 378–390.
Mikhailov, A.C.& Krinskii, V.I. (1983). Physica D9, 346–371.
Meron, E. & Pelcé, P. (1988). Phys. Rev. Lett. 60, 1880–1883.
Vidal, C. & Hanusse, P. (1986). Int. rev. Phys. Chem. 5, 1–155.
Field, R.J. & Burger, M. (eds.) (1985). Oscillations and travelling waves in chemical systems. Wiley: New York.
Tyson, J. & Keener, J. (1988). Physica D32, 327–361.
Hanusse, P. (1987). J. Chim. Phys. 84, 1315–1327.
Hanusse, P. & Guillataud, P. Object detection and identification by hierarchical segmentation, to be published.
Marsden, J.E. & McCracken, M. (1976). The Hopf bifurcation and its applications. Springer.
Guckenheimer, J. & Holmes, P. (1983). Nonlinear oscillations, Dynamical sytems, Bifurcations of vector fields, Vol. I. Springer.
Golubitsky, M. & Schaeffer, D.G. (1985). Singularities and groups in bifurcation theory. Springer.
de Kepper, P., Pacault, A. & Rossi, A. (1976). C.R. Acad. Sci. Paris 282C, 199.
FitzHugh, R. (1960). J. Gen. Physiol. 43, 867–896.
Kuramoto, Y. (1976). Prog. Theor. Phys. 56, 724–740.
Boissonade, J. & de Kepper, P. (1981). J. Chem. Phys. 75, 189–195.
Hanusse, P. & Perez-Muñuzuri, V., to be published.
Winfree, A.T., Winfree, E.M. & Seifert, H. (1985). Physica D17, 109.
Wolfram, S. (1986). Theory and applications of Cellular Automata. World Scientific: Singapore.
Markus, M., see contribution in this volume.
Hanusse, P. & Pérez-Muñuzuri, V., in preparation.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1991 Springer Science+Business Media New York
About this chapter
Cite this chapter
Hanusse, P., Pérez-Muñuzuri, V., Vidal, C. (1991). Phase Dynamics and Spatial Patterns in Oscillating and Excitable Media. In: Holden, A.V., Markus, M., Othmer, H.G. (eds) Nonlinear Wave Processes in Excitable Media. NATO ASI Series, vol 244. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-3683-7_44
Download citation
DOI: https://doi.org/10.1007/978-1-4899-3683-7_44
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4899-3685-1
Online ISBN: 978-1-4899-3683-7
eBook Packages: Springer Book Archive