Abstract
A practical method was proposed recently for finding local bifurcation points in an n-dimensional vector field F by seeking their ‘underlying catastrophes’. Here we apply the idea to a partial differential equation as an example of the role that catastrophes can play in reaction diffusion. What are these ‘underlying’ catastrophes? We then show they essentially define a restricted class of ‘solvable’ rather than ‘all classifiable’ singularities, by identifying degenerate zeros of a vector field F without taking into account its vectorial character. As a result they are defined by a minimal set of r analytic conditions that provide
a practical means to solve for them, and a huge reduction from the calculations needed to classify a singularity, which we will also enumerate here. In this way, underlying catastrophes seem to allow us apply Thom’s elementary catastrophes in much broader contexts.
a practical means to solve for them, and a huge reduction from the calculations needed to classify a singularity, which we will also enumerate here. In this way, underlying catastrophes seem to allow us apply Thom’s elementary catastrophes in much broader contexts.
Original language | English |
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Article number | 085005 |
Number of pages | 22 |
Journal | Nonlinearity |
Volume | 37 |
Issue number | 8 |
Early online date | 20 Jun 2024 |
DOIs | |
Publication status | Published - 1 Aug 2024 |
Bibliographical note
Publisher Copyright:© 2024 The Author(s).
Research Groups and Themes
- Engineering Mathematics Research Group