Hopf Bifurcation–Driven Chiral Amplification in an Oregonator-Based Oscillatory Chemical System with Optimal Control of Time-Scale Separation

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Year : 2026 | Volume : 17 | 03 | Page :
By

Lakshmi. N. Sridhar,

  1. Professor, Department of Chemical Engineering, University of Puerto Rico, Mayaguez, Puerto Rico, United States

Abstract

Nonlinear chemical systems exhibiting oscillatory kinetics and symmetry-breaking behavior have been widely studied in the context of reaction–diffusion chemistry and crystallization processes. However, the interaction between oscillatory dynamics and chiral amplification mechanisms remains insufficiently understood within a unified dynamical systems framework. This work aims to develop and analyze a reduced-order nonlinear model that couples an Oregonator-type activator–inhibitor system with a chiral response variable, and to investigate the role of Hopf bifurcation and time-scale modulation in enhancing chiral response under optimal operating conditions. A three-state dynamical system consisting of activator concentration , inhibitor concentration , and chiral imbalance is formulated with a time-scale separation parameter . The nonlinear behavior of the system is investigated by deriving the Jacobian analytically and applying MATCONT continuation to locate Hopf bifurcations. Eigenvalue calculations and first Lyapunov coefficients are then used to characterize the stability and nature of the detected bifurcations. The control problem is formulated and solved in Pyomo.DAE, with the designated forcing parameter serving as the time-dependent control variable. To account for stability during optimization, a neural-network model constructed from the bifurcation dataset is used as a surrogate for the system’s local stability behavior thereby supporting reliable prediction and effective stability-aware process optimization.

Keywords: Chiral crystallization, Oregonator model, Hopf bifurcation, nonlinear chemical oscillations, optimal control

How to cite this article: Lakshmi. N. Sridhar. Hopf Bifurcation–Driven Chiral Amplification in an Oregonator-Based Oscillatory Chemical System with Optimal Control of Time-Scale Separation. Journal of Control & Instrumentation. 2026; 17(03):-.
How to cite this URL: Lakshmi. N. Sridhar. Hopf Bifurcation–Driven Chiral Amplification in an Oregonator-Based Oscillatory Chemical System with Optimal Control of Time-Scale Separation. Journal of Control & Instrumentation. 2026; 17(03):-. Available from: https://journals.stmjournals.com/joci/article=2026/view=259637

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Ahead of Print Subscription Review Article
Volume 17
03
Received 19/09/2026
Accepted 05/10/2026
Published 09/10/2026
Publication Time 20 Days

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