Bifurcation analysis of the Nowak–Bangham model in CTL dynamics

Egami, Chikahiro

doi:10.1016/j.mbs.2009.06.005

Cited by 8 publications

(1 citation statement)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This section introduces a Hopf bifurcation theorem established by Liu [11] without the proof. In [1], the author developed the techniques to apply Liu's theorem to a higher-order system with a rigorous computation through the bifurcation analysis for CTL dynamics.…”

mentioning

confidence: 99%

Mechanism for the color transition of the Belousov-Zhabotinsky reaction catalyzed by cerium ions and ferroin

Egami¹

2018

Discrete &Amp; Continuous Dynamical Systems - B

Self Cite

View full text Add to dashboard Cite

The oscillation property of the Belousov-Zhabotinsky reaction and the color transition of its solution depend on the catalytic action of the metal ions. The solution of the reaction system catalyzed by both cerium ions and ferroin has a more complicated effect on the color than either the ceriumcatalyzed case or the ferroin-catalyzed case. To theoretically elucidate the color transition of the case catalyzed by these two ions, a reduced model consisting of three differential equations is proposed, incorporating both the Rovinsky-Zhabotinsky scheme and the Field-Körös-Noyes scheme simplified by Tyson [Ann. N.Y. Acad. Sci., 316 (1979), pp.279-295]. The presented model can have a limit cycle under reasonable conditions through a Hopf bifurcation, and its existence theorem is proven by employing the bifurcation criterion established by Liu [

show abstract

mentioning

confidence: 99%