Mushroom Bifurcation
Definition 1
A bifurcation that consists of four saddle-node bifurcations and whose bifurcation diagram looks like a mushroom is called a mushroom bifurcation.
Explanation 2
Fundamentally, the mushroom bifurcation is not a new bifurcation, but that very fact is the reason one should know about mushroom bifurcations. One may encounter a bifurcation that seems new at first glance, but by dissecting it in detail one can regard it as a combination of already well-known bifurcations; nevertheless, one should be aware that it may still be given a new name.
Fucho-Rius, M., Maretvadakethope, S., Haro, À., Alarcón, T., Sardanyés, J., & Pérez-Carrasco, R. (2025). Local nearby bifurcations lead to synergies in critical slowing down: The case of mushroom bifurcations. Physical Review E, 111(2), 024213. https://doi.org/10.1103/PhysRevE.111.024213 ↩︎
Otero-Muras, I., Perez-Carrasco, R., Banga, J. R., & Barnes, C. P. (2023). Automated design of gene circuits with optimal mushroom-bifurcation behavior. Iscience, 26(6). https://doi.org/10.1016/j.isci.2023.106836 ↩︎