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.

In this article, we have considered the Finsler space \(F^{n}\,(n>2)\) with a Generalized Matsumoto metric and found the necessary and sufficient criteria for it to be of Douglas type. We have also demonstrated the condition for the mentioned metric in Finsler space to become a Berwald space. The space is also projectively flat if it is a Berwald space.

In this article, we consider the Finsler space Fn (n > 2) with an infiniteseries (α, β)-metric and establish the necessary and sufficient conditions for it to be of Douglas type. Additionally, we demonstrate the criteria under which this metric in a Finsler space becomes a Berwald space. Furthermore, the space is shown to be projectively flat if it is a Berwald space.