Abstract
Spatio-temporal phenomena in nonlinear systems have been found to be of great variety including periodic and chaotic structures.1 We shall find here that the method of Pade' approximants may be extended to describe some of these phenomena including the chemical center wave. Catastrophe (or more generally singularity) theory is also shown here to be of great utility in obtaining classification theorems for systems with multiple space or time scales. The idea of symmetry broken singularities is introduced. Finally, unlike in the case of ordinary differential systems, it is shown that in some cases the phenomena must be understood in terms of the geometry of function space via "behavior functionals". These ideas shall be introduced through a discussion of various physical problems including crystal growth and reaction diffusion systems.
Keywords
- Topological Feature
- Reaction Diffusion System
- Slow Manifold
- Behavior Surface
- Homogeneous Steady State
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Ortoleva, P. (1980). Dynamic Pade' approximant and behavior singularities in nonlinear physico-chemical systems. In: Bardos, C., Lasry, J.M., Schatzman, M. (eds) Bifurcation and Nonlinear Eigenvalue Problems. Lecture Notes in Mathematics, vol 782. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090436
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DOI: https://doi.org/10.1007/BFb0090436
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