Study stabilizability and solvability for chemical kinetics of the delayed oregonator model


Abstract views: 17 / PDF downloads: 25

Authors

  • Mayadah Khalil Ghaffar Department of Physics, College of Science, Tikrit University, Tikrit

Keywords:

Chemical reaction, DDE, Backstepping method, Mass – Action law, chain approximation, Lyapunov, Controller

Abstract

Delays naturally appear in chemical reactions and they are often responsible for presence of complex behaviours, we will be take delay effects in Beulosuv-Zhabotonksiy reaction this mechanism is represented by a simple model, called the Oregonator model. Chemical kinetics of the considered Oregonator model will be taken by use of delay mass-action law and study the stabilizability and solvability by backstepping method after formally introduce the chain approximation for kinetic scheme of delayed Oregonator model. We will compar stabilizability results output between backstepping with method of steps and backstepping with chain method

References

Chellaboina, V., Bhat, S. P., Haddad, W. M., & Bernstein, D. S. (2009). Modeling and analysis of mass-action kinetics. IEEE Control Systems Magazine, 29(4), 60–78.

Érdi, P., & Tóth, J. (1989). Mathematical models of chemical reactions: theory and applications of deterministic and stochastic models. Manchester University Press.

Fridman, E., (2014), Introduction to Time-Delay Systems: Analysis and control. Springer

Ghaffar, M. K., Fadhel, F. S., & Arif, N. E. (2022, August). Application of the generalized backstepping control method for lotka-volterra prey-predator system with constant time delay. In Journal of Physics: Conference Series (Vol. 2322, No. 1, p. 012012). IOP Publishing.

Haddad, W. M., Chellaboina, V., & Hui, Q. (2010). Nonnegative and compartmental dynamical systems. Princeton University Press.

Han, Q.-L. and Yu, L., (2004), Robust Stability of Linear Neutral the systems with Nonlinear Parameter Perturbations. IEE Proceedings-Control Theory and Applications, 151(5), 539–546

Horn, F., & Jackson, R. (1972). General mass action kinetics. Archive for rational mechanics and analysis, 47, 81–116.

Krasznai, B., Győri, I., & Pituk, M. (2010). The modified chain method for a class of delay differential equations arising in neural networks. Mathematical and computer modelling, 51(5–6), 452–460.

Lipták, G., Hangos, K. M., & Szederkényi, G. (2018). Approximation of delayed chemical reaction networks. Reaction Kinetics, Mechanisms and Catalysis, 123, 403–419.

Ma, W., M.Song, Y.Takeuchi, (2004) Global stability of an SIR epidemic model with time delay. Applied Mathematics Letters pp. 1141–1145.

Muralidharan, J. “Advancements in 5G Technology: Challenges and Opportunities in Communication Networks.” Progress in Electronics and Communication Engineering 1.1 (2024): 1–6.

Vinod, G. V., D. Vijendra Kumar, and N. M. Ramalingeswararao. “An Innovative Design of Decoder Circuit using Reversible Logic.” Journal of VLSI circuits and systems 4.01 (2022): 1–6.

Orosz, G., Wilson, R. E., & Stépán, G. (2010). Traffic jams: dynamics and control. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 368(1928), 4455–4479.

Manthila, Perera, K. Madugalla Anuradha, and Rasanjani Chandrakumar. “Ultra-Short Waves Using Beam Transmission Methodology.” National Journal of Antennas and Propagation 4.1 (2022): 1–7.

Ünal, H. U. (2018). QUALITATIVE ANALYSIS OF DELAYED-CONCENTRATION IN OREGONATOR-BASED CHEMICAL OSCILLATORS. Eskişehir Technical University Journal of Science and Technology A-Applied Sciences and Engineering, 19(3), 637-644.

Downloads

Published

2024-11-14

How to Cite

Mayadah Khalil Ghaffar. (2024). Study stabilizability and solvability for chemical kinetics of the delayed oregonator model. Results in Nonlinear Analysis, 7(4), 93–103. Retrieved from https://nonlinear-analysis.com/index.php/pub/article/view/560