Global bifurcation in the Brusselator system

Gaussian approximations for stochastic systems with delay: Chemical Langevin equation and application to a Brusselator system

“…[31][32][33][34] Previous work on stochastic versions of the Brusselator model include the study of fluctuations about limit cycles, 28 pattern formation in spatial variants, 5 and a recent study on noise-induced switching between large and small amplitude oscillations. 35 We here study a non-Markovian variation of the Brusselator model.…”

Global Attractor of a Coupled Two-Cell Brusselator Model

“…Brusselator kinetics describes the following scheme of chemical reactions There are several known examples of autocatalysis which can be modeled by the Brusselator equations, such as ferrocyanide-iodate-sulphite reaction, chlorite-iodide-malonic acid reaction, arsenite-iodate reaction, some enzyme catalytic reactions, and fungal mycelia growth, cf. [1,2,5,9].…”

“…Numerous studies by numerical simulations or by mathematical analysis, especially after the publications [22,23] in 1993, have shown that the autocatalytic reaction-diffusion systems such as the Brusselator equations and the Gray-Scott equations [13,14] exhibit rich spatial patterns (including but not restricted to Turing patterns) and complex bifurcations [1,4,5,7,8,11,16,24,26,38] as well as interesting dynamics [6,9,10,17,21,[27][28][29]39,40] on 1D or 2D domains.…”

Multiple bifurcations and spatiotemporal patterns for a coupled two-cell Brusselator model

“…It is well-known that the reaction-diffusion system with autocatalytic such as the Brusselator equations and the Gray-Scott equations [1,2] can exhibit rich spatial patterns (including but not restricted to Turing patterns) [3,4,5,6,7]. One of the most widely studied models is the Brusselator system, which describes the following chemical reactions:…”