# Stability, convergence and bifurcation in some models of chemical kinetics

Source: [Stability, convergence and bifurcation in some models of chemical kinetics](<https://www.sota2.com/research/paper/68fa57f61e209131ce9a9fde>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T15:02:39.743Z

Authors: Abuthahir Abdulrahuman, Kalyan Chakrabarti, Gaurav Raina

Published: 2021-03-24T06:50:18.000Z

## Abstract

In this paper, we analyze the stability, convergence, and bifurcation properties of the Boissonade-De Kepper (BD) model which played a key role in the development of nonlinear chemical dynamics. We first outline conditions for local stability, which may help guide design considerations. Then, we show that the BD model undergoes a Hopf bifurcation when the stability condition gets violated. Using Poincar\\'{e} normal forms and center manifold theory, we derive explicit analytic expressions for determining the type of the Hopf bifurcation and the stability of the limit cycles. This provides insights on the system dynamics just beyond the stable regime. Some of the analytical insights are corroborated with numerical computations. We also show that the mathematical results obtained in this paper may have wider applicability beyond the BD model.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2103.13016>)

[PDF](<https://arxiv.org/pdf/2103.13016.pdf>)