Not answering your question specifically, it seems that the cusp method of bifucation seems the popular choice of the seven types of catastrophe of René Thom, perhaps due to the fact that it can produce irregular outcomes and sudden ones as prevalent in catastrophe theory, such as by Joseph, J. Jacobson (2020) in ‘Cusp Catastrophe Model of Climate Change - Companion to Basic Global Warming’. The Journal of Business, Economics, Sustainability, Leadership and Innovation, 16th January, 2019(2). Available at: https://besli.pubpub.org/pub/cuspcatastrophe/release/3. Jacobson interestingly applies this as a postulation that reliance on linear prognostication to do with global warming may miss a trick and also suggests that sudden changes could and should be matched by suitable premptive behaviour. Could it be a suggestion that you innovate application of the swallow tail type as regards this vital area of research of global warming/ climate change, where perhaps this has not been done before, perhaps because it might suggest a stable or relatively stable outcome? Just a thought. Good luck.

Thank you so much, Grant Gover

Oluma Ararso you're welcome

Dear doctor

Go To

Swallowtail-type diffraction catastrophe beams

Houan Teng, Yixian Qian, Yanping Lan, and Wentao Cui

• Optics Express
• Vol. 29,
• Issue 3,
• pp. 3786-3794
• (2021)
• https://doi.org/10.1364/OE.416134

"Abstract

We demonstrate a universal approach for generating high-order diffraction catastrophe beams, specifically for Swallowtail-type beams (abbreviated as Swallowtail beams), using diffraction catastrophe theory that was defined by potential functions depending on the control and state parameters. The three-dimensional curved caustic surfaces of these Swallowtail catastrophe beams are derived by the potential functions. Such beams are generated by mapping the cross sections of the high-order control parameter space to the corresponding transverse plane. Owing to the flexibility of the high-order diffraction catastrophe, these Swallowtail beams can be tuned to a diverse range of optical light structures. Owing to the similarity in their frequency spectra, we found that the Swallowtail beams change into low-order Pearcey beams under given conditions during propagation. Our experimental results are in close agreement with our simulated results. Such fantastic catastrophe beams that can propagate along curved trajectories are likely to give rise to new applications in micromachining and optical manipulation, furthermore, these diverse caustic beams will pave the way for the tailoring of arbitrarily accelerating caustic beams."