@article{oai:kansai-u.repo.nii.ac.jp:00018921,
 author = {Gotoh, Fumitoshi and Generalis, Sotos C. and Itano, Tomoaki},
 journal = {Science and technology reports of Kansai University = 関西大学理工学研究報告},
 month = {Mar},
 note = {Spiral states are commonly observed in pattern formation on a sphere. Li et al.(Phys. Rev. E, Vol.71, 016301 [2005]) previously proposed a method to generate the spiral states by adopting mixed modes with adjacent wavenumbers like l = l0, l0 + 1, as the initial condition of a time-developing numerical simulation. Herein, using the Swift-Hohenberg equation as an example, we show that Li's empirical method can be successful only in particular regions of parameter space. Tracing the state by a continuation method generated from the static state via three symmetry breakings, the spiral state may be regarded as a resonant state generated by the combination of a few degenerate unstable modes with different azimuthal wave numbers., This work has been supported in part by KAKENHI (20K04294).},
 pages = {13--20},
 title = {Numerical exploration of the spiral state in the pattern formation of the Swift-Hohenberg equation on a sphere},
 volume = {63},
 year = {2021}
}