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Reversible chemical reactions model with fractional difference operator: Dynamical analysis and synchronization.
1Cyber Security and Digital Industrial Revolution Centre, Universiti Pertahanan Nasional Malaysia, Kem, Sungai Besi, 57000 Kuala Lumpur, Malaysia.
Chaos (Woodbury, N.Y.)
|April 1, 2023
Summary
This study models two-step reversible chemical reactions using fractional calculus, revealing chaotic dynamics and enabling subsystem synchronization. These findings have applications in biofuel production from vegetable oils and animal fats.
Area of Science:
- Chemical kinetics
- Mathematical modeling
- Fractional calculus
Background:
- Chemical reactions are fundamental to life, with understanding their complex dynamics crucial for real-world applications.
- Reversible chemical reactions, like ester hydrolysis and salt formation, are vital in industrial processes.
Purpose of the Study:
- To develop a mathematical model for two-step reversible chemical reactions using a Caputo fractional difference operator.
- To analyze the chaotic behavior and synchronization of the proposed chemical reaction model.
Main Methods:
- Construction of a mathematical model incorporating a Caputo fractional difference operator.
- Analysis of chaotic responses using bifurcation diagrams and time-varying plots.
- Investigation of system periodicity using maximum Lyapunov exponents and Jacobian matrix.
- Achieving subsystem synchronization via nonlinear control functions.
Main Results:
- Demonstrated chaotic behavior in the system for both identical and non-identical fractional orders.
- Illustrated periodic state changes and confirmed chaos with Lyapunov exponents.
- Successfully synchronized subsystems using nonlinear control strategies.
- Presented numerical simulations comparing commensurate and incommensurate order models.
Conclusions:
- The fractional-order mathematical model effectively captures the complex dynamics of two-step reversible chemical reactions.
- The study provides insights into chaotic dynamics and synchronization, with potential applications in biofuel production.
- Understanding these fractional-order dynamics is significant for optimizing transesterification reactions in biofuel synthesis.
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