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Kosambi–Cartan–Chern Stability in the Intermediate Nonequilibrium Region of the Brusselator Model

Yamasaki, Kazuhito 山崎, 和仁 ヤマサキ, カズヒト Yajima, Takahiro 神戸大学

2022.02

概要

This study applies the Kosambi–Cartan–Chern (KCC) theory to the Brusselator model to derive differential geometric quantities related to bifurcation phenomena. Based on these geometric quantities, the KCC stability of the Brusselator model is analyzed in linear and nonlinear cases to determine the extent to which nonequilibrium affects bifurcation and stability. The geometric quantities of the Brusselator model have a constant value in the linear case, and are functions of spatial variables with parameter dependence in the nonlinear case. Therefore, the KCC stability of the nonlinear case shows various distribution patterns, depending on the distance from the equilibrium point (EQP), as follows: in the regions near or far enough from the EQP, the distribution of KCC stability is uniform and regular; and in the intermediate nonequilibrium region, the distribution varies and shows complex patterns with parameter dependence. These results indicate that stability in the intermediate nonequilibrium region plays an important role in the dynamic complex patterns in the Brusselator model.

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参考文献

Sab˘au, S.V. [2005b] “Systems biology and deviation curvature tensor,” Nonlinear Anal. RWA. 6, 563–587.

Salnikova, T. V., Kugushev, E. I. & Stepanov, S. Y. [2020] “Jacobi Stability of a Many-Body System with

Modified Potential,” Doklady Mathematics 101, 154–157.

Sarmah, H. K., Das, M. C. & Baishya, T. K. [2015] “Hopf bifurcation in a chemical model,” Int. J. Innov.

Res. Sci. Eng. Technol. 1, 23–33.

Sulimov, V. D., Shkapov, P. M. & Sulimov, A. V. [2018] “Jacobi stability and updating parameters of

dynamical systems using hybrid algorithms,” IOP Conf. Ser. Mater. Sci. Eng. 468, 012040.

Thompson, J.M.T. [1982] Instabilities and Catastrophes in Science and Engineering (John Willy & Sons,

New York).

Twizell, E. H., Gumel, A. B. & Cao, Q. [1999] “A second-order scheme for the “Brusselator” reactiondiffusion system,” J. Math. Chem. 26, 297–316.

Taylor, A. F. [2002] “Mechanism and phenomenology of an oscillating chemical reaction,” Prog. React.

Kinet. Mec. 27, 247–326.

Udri¸ste, C. & Nicola, I.R. [2009] “Jacobi stability of linearized geometric dynamics,” J. Dynam. Syst.

Geomet. Theo. 7, 161–173.

Yamasaki, K. & Yajima, T. [2013] “Lotka-Volterra system and KCC theory: Differential geometric structure

of competitions and predations,” Nonlinear Anal. RWA. 14, 1845–1853.

Yamasaki, K. & Yajima, T. [2016] “Differential geometric structure of non-equilibrium dynamics in competition and predation: Finsler geometry and KCC theory,” J. Dynam. Syst. Geomet. Theo. 14,

137–153.

Yamasaki, K. & Yajima, T. [2017] “KCC analysis of the normal form of typical bifurcations in onedimensional dynamical systems: geometrical invariants of saddle-node, transcritical, and pitchfork

bifurcations,” Int. J. Bifurcat. Chaos, 27, 1750145.

Yamasaki, K. & Yajima, T. [2020] “KCC analysis of a one-dimensional system during catastrophic shift of

the Hill function: Douglas tensor in the nonequilibrium region,” Int. J. Bifurcat. Chaos, 30, 2030032.

Zhabotinsky, A. M. [1964] “Periodical oxidation of malonic acid in solution (a study of the Belousov reaction

kinetics),” Biofizika 9 306–311.

Zhao, Z. & Ma, R. [2019] “Local and global bifurcation of steady states to a general Brusselator model,”

Adv. Differ. Equ. No. 491 1–14.

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