Detecting Critical Point of Fractional-Order Chemical System with Synchronization and Application to Image Enhancement Technique

In chemical reactions, not all the reactants interact immediately, and thus, there is a need to predict the critical point of a chemical reaction. In this paper, a new fractional-order Willamowski–Ro¨\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ddot{o}$$\end{document}ssler chemical system is studied to predict the critical point in the chemical reaction. Consequently, the existence of chaotic or non-equilibrium phenomenon in the proposed chemical system is confirmed. Also, the reaction ratio of the reactants in this chemical system is investigated. In addition, the necessary conditions are derived to synchronize two identical chemical systems by designing and applying sliding mode control. Further, we have shown that the proposed synchronization technique is faster than the existing synchronization technique by comparing sliding mode controller. In application point of view, the described fractional-order chemical system is applied for image enhancement technique. Finally, numerical simulations are provided to validate the effectiveness of the proposed theoretical approach.