Abstract
In a recent paper, Bigge and Bohl [2] found some interesting bifurcation diagrams for a discrete diffusion reaction model. We give an interpretation of their results from the view of singularity theory and we will also indicate how this theory may be used to set up numerical methods for singular solutions such as bifurcation points or isolated points.
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
Beyn, W.-J.: On discretizations of bifurcation problems. pp. 46–73 in Bifurcation problems and their numerical solution (Eds.: H.D. Mittelmann, H. Weber), ISNM 54, Birkhäuser Verlag, 1980.
Bigge, J., Bohl, E.: On the steady states of finitely many chemical cells (submitted).
Bohl, E.: Finite Modelle gewöhnlicher Randwertaufgaben. LAMM Bd. 51, Teubner Verlag, Stuttgart, 1981.
Golubitsky, M., Guillemin, V.: Stable mappings and their singularities. Graduate Texts in Mathematics No. 14, Springer Verlag, New York, 1974.
Golubitsky, M., Schaeffer, D.: A theory for imperfect bifurcation via singularity theory. Commun. Pure Appl. Math. 32, 21–98, 1979.
Martinet, J.: Deploiements versels des applications differentiables et classification des applications stables. pp. 1–44, Lecture Notes in Mathematics 535, Springer Verlag, 1976.
Moore, G.: The numerical treatment of non-trivial bifurcation points. Numer. Funct. Anal. Optimiz. 2, 441–472, 1980.
Poston, T., Stewart, I.: Catastrophe theory and its applications. Pitman, London, 1978.
Vainberg, M.M., Trenogin, V.A.: The methods of Lyapunov and Schmidt in the theory of non-linear equations and their further development. Russian Math. Surveys 17, 1–60, 1962.
Weber, H.: On the numerical approximation of secondary bifurcation points. pp. 407–425, Lecture Notes in Mathematics 878, Springer Verlag, 1981.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1983 Springer-Verlag
About this paper
Cite this paper
Beyn, W.J. (1983). Numerical analysis of singularities in a diffusion reaction model. In: Knobloch, H.W., Schmitt, K. (eds) Equadiff 82. Lecture Notes in Mathematics, vol 1017. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0103239
Download citation
DOI: https://doi.org/10.1007/BFb0103239
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-12686-7
Online ISBN: 978-3-540-38678-0
eBook Packages: Springer Book Archive