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Dergiler / An International Journal of Optimization and Control: Theories & Applications (IJOCTA) / 2023 / Cilt: 13 - Sayı: 1

A simple method for studying asymptotic stability of discrete dynamical systems and its applications

Tuan Manh
Thi Kim Quy Ngo
Ha Hai Truong
Sayfa
10–25
Yayın Tarihi
2023-12-17
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Finally, a set of numerical examples are performed to illustrate and support the theoretical findings.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this work, we introduce a simple method for investigating the asymptotic stability of discrete dynamical systems, which can be considered as an extension of the classical Lyapunov's indirect method.
📊
Temel Bulgular & Veri:This method is constructed based on the classical Lyapunov's indirect method and the idea proposed by Ghaffari and Lasemi in a recent work.
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Sonuç & Katkı:Finally, a set of numerical examples are performed to illustrate and support the theoretical findings.
🔬Tür:Modelleme & Sayısal Simülasyon
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

In this work, we introduce a simple method for investigating the asymptotic stability of discrete dynamical systems, which can be considered as an extension of the classical Lyapunov's indirect method. This method is constructed based on the classical Lyapunov's indirect method and the idea proposed by Ghaffari and Lasemi in a recent work. The new method can be applicable even when equilibia of dynamical systems are non-hyperbolic. Hence, in many cases, the classical Lyapunov's indirect method fails but the new one can be used simply. In addition, by combining the new stability method with the Mickens' methodology, we formulate some nonstandard finite difference (NSFD) methods which are able to preserve the asymptotic stability of some classes of differential equation models even when they have non-hyperbolic equilibrium points. As an important consequence, some well-known results on stability-preserving NSFD schemes for autonomous dynamical systems are improved and extended. Finally, a set of numerical examples are performed to illustrate and support the theoretical findings.

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Bu Makaleye Atıf Yap

Manh, T., Ngo, T. K. Q., Truong, H. H. (2023). A simple method for studying asymptotic stability of discrete dynamical systems and its applications. An International Journal of Optimization and Control: Theories & Applications (IJOCTA), Cilt: 13 - Sayı: 1, 10–25. https://doi.org/10.11121/ijocta.2023.1243

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Kaynakça (15)

  1. Allen. L. J. S. An Introduction to Mathe- matical Biology. Prentice Hall, Upper Saddle River, NJ
  2. Diethelm, K. The Analysis of Fractional Dif- ferential Equations: An Application-Oriented Exposition Using Differential Operators of Caputo Type. Springer, Berlin, Heidelberg, 2010
  3. Khalil, H. K. (2022). Nonlinear Systems. 3rd Edition, Pearson
  4. Kilbas, A. A., Srivastava, H. M., & Trujillo, J. J. (2006). Theory and Applications of Frac- tional Differential Equations, Elsevier
  5. LaSalle, J. P. (1976). The Stability of Dynam- ical Systems. Society for Industrial and Ap- plied Mathematics, Philadelphia, PA
  6. Perko. L. (2001). Differential Equations and Dynamical Systems, Springer, New York
  7. Podlubny. I. (1999). Fractional Differential Equations. Academic Press, San Diego
  8. Stuart, A., & Humphries. A. R. (1998). Dynamical Systems and Numerical Analysis. Cambridge University Press
  9. Alzabut. J., Tyagi. S., & Martha. S. C. (2020). On the stability and Lyapunov direct method for fractional difference model of BAM neu- ral networks. Journal of Intelligent & Fuzzy Systems, 38(3), 2491-2501
  10. Alzabut. J., Tyagi. S., & Abbas. S. (2020). Discrete fractional-order BAM neural net- works with leakage delay: existence and sta- bility results. Asian Journal of Control, 22(1), 143-155
  11. Alzabut. J., George Maria Selvam. A, Dhi- neshbabu. R., Tyagi. S., Ghaderi. M., & Reza- pour. S. (2022). A Caputo discrete fractional- order thermostat model with one and two sensors fractional boundary conditions de- pending on positive parameters by using the Lipschitz-type inequality. Journal of Inequali- ties and Applications, (2022), Article number: 56
  12. Alzabut. J., George Maria Selvam. A., Dhakshinamoorthy. V., Mohammadi. H., & Rezapour, S. (2022). On chaos of dis- crete time fractional order host-immune- tumor cells interaction model. Journal of Applied Mathematics and Computing,
  13. Dianavinnarasi. J., Raja. R., Alzabut. J., Cao. J., Niezabitowski. M., & Bagdasar, O. (2022). Application of Caputo–Fabrizio operator to suppress the Aedes Aegypti mosquitoes via Wolbachia: An LMI approach. Mathematics and Computers in Simulation, 201, 462-485
  14. Goufo. E. F. D., Ravichandran. C., & Bira- jdar. G. A. (2021). Self-similarity techniques for chaotic attractors with many scrolls using step series switching. Mathematical Modelling and Analysis, 26(4), 591-611
  15. Iswarya. M., Raja, R., Cao, J., Niez- abit