KCC Theory of the Oregonator Model for Belousov-Zhabotinsky Reaction

被引:1
作者
Gupta, M. K. [1 ]
Sahu, Abha [1 ]
Yadav, C. K. [1 ]
Goswami, Anjali [2 ]
Swarup, Chetan [2 ]
机构
[1] Guru Ghasidas Vishwavidyalaya, Dept Math, Bilaspur 495009, India
[2] Saudi Elect Univ, Coll Sci & Theoret Studies, Dept Basic Sci, Riyadh 11673, Saudi Arabia
关键词
Oregonator model; KCC theory; Berwald connection; Jacobi stability; JACOBI STABILITY; OSCILLATIONS; SYSTEMS; VIEW;
D O I
10.3390/axioms12121133
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The behavior of the simplest realistic Oregonator model of the BZ-reaction from the perspective of KCC theory has been investigated. In order to reduce the complexity of the model, we initially transformed the first-order differential equation of the Oregonator model into a system of second-order differential equations. In this approach, we describe the evolution of the Oregonator model in geometric terms, by considering it as a geodesic in a Finsler space. We have found five KCC invariants using the general expression of the nonlinear and Berwald connections. To understand the chaotic behavior of the Oregonator model, the deviation vector and its curvature around equilibrium points are studied. We have obtained the necessary and sufficient conditions for the parameters of the system in order to have the Jacobi stability near the equilibrium points. Further, a comprehensive examination was conducted to compare the linear stability and Jacobi stability of the Oregonator model at its equilibrium points, and We highlight these instances with a few illustrative examples.
引用
收藏
页数:16
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