KaydedilenlerDerginizi ekleyin

Dergiler / Turkish Journal of Mathematics and Computer Science / 2026 / Volume: 11 Special Issue

Investigation of Lorenz Equation System with Variable Step Size Strategy

Saniye İnce Polat(Sehit Mustafa Cuhadar Secondary School)0000-0003-3832-2235
Gülnur Çelik Kızılkan(Necmettin Erbakan University)0000-0003-1538-082X
Sayfa
—
Yayın Tarihi
2019-12-30
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

The effectiveness of the variable step size strategy for the solution of this chaotic system has been discussed.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this study, variable step size strategy has been considered to analyze the numerical solution of the Lorenz system with chaotic structure.
📊
Temel Bulgular & Veri:Phase portraits have been obtained for this chaotic system.
💡
Sonuç & Katkı:The effectiveness of the variable step size strategy for the solution of this chaotic system has been discussed.
🔬Tür:Conference Paper
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Lorenz systems · numerical solution · variable step size

Abstract

In this study, variable step size strategy has been considered to analyze the numerical solution of the Lorenz system with chaotic structure. Phase portraits have been obtained for this chaotic system. The effectiveness of the variable step size strategy for the solution of this chaotic system has been discussed.

🔖

Bu Makaleye Atıf Yap

Polat, S. İ., Kızılkan, G. Ç. (2019). Investigation of Lorenz Equation System with Variable Step Size Strategy. Turkish Journal of Mathematics and Computer Science, Volume: 11 Special Issue. https://ajindex.com/articles/1324866

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (16)

  1. Afacan, E., Yard{\i}m, F.E., {\em Simulation of a communication system using Lorenz-based differential chaos shift keying (DCSK)model}, J. Fac. Eng. Arch. Gazi Univ., \textbf{25(1)}(2010), 101--110.
  2. Christodoulou N.S., {\em An algorithm using Runge- Kutta methods of orders 4 and 5 for systems of ODEs}, IJNMA, \textbf{2(1)}(2009), 47--57.
  3. \c{C}elik, K., Kurt, E., A new image encryption algorithm basd on Lorenz system, Electronics, Computers and Artificial Intelligence, International Conference-8th edition, 30 June-02 July, Bucharest, Romania, 2016.
  4. \c{C}elik K{\i}z{\i}lkan, G., Step size strategies on the numerical integration of the systems of differential equations, Ph.D. Thesis, Selcuk University Graduate Natural and Applied Sciences, Konya, 2009 (in Turkish).
  5. \c{C}elik K{\i}z{\i}lkan, G., Ayd{\i}n, K., {\em Step size strategies for the numerical integration of systems differential equations}, J. Comput. Appl. Math., \textbf{236(15)}(2012), 3805--3816.
  6. El- Basha, O., El- Shahat, A. Fayed, H.,{\em Chaos theory and Lorenz attractors}, Sohag Journal of Sciences, \textbf{(1)(1)}(2016), 7--12.
  7. Guellal, S., Grimalt, P., Cherruault, Y., {\em Numerical Study of Lorenz’ s equation by the Adomian method}, Computers Math. Applic., \textbf{(33)(3)}(1997), 25--29.
  8. Guran, A., Ahmadi, G., {\em An Enchanced numerical solution of the Lorenz system by means of the differential Quadrature Method}, AMIM, \textbf{(17)(1)} (2012), 16--30.
  9. Hateley, J., The Lorenz System, Lecture Notes, http://web.math.ucsb.edu/~jhateley/paper/lorenz.pdf, (Access date: 23.09.2019).
  10. \.{I}nce Polat, S., Evaluation of approximate solutions of the Lorenz system, Master Thesis, The Graduate School of Natural and Aplied Science of Necmettin Erbakan University, Konya, 2019 (in Turkish).
  11. Li, J., Wang, Y., Zhang, W., {\em Numerical simulation of the Lorenz-type chaotic system using Barycentric Lagrange interpolation collocation method}, Hindawi Advances in Mathematical Physics, \textbf{(2019)}(2019), 1--10.
  12. Lorenz, E.N., {\em Deterministic nonperiodic flow}, Journal of the Atmospheric Sciences, \textbf{20}(1963), 130--141.
  13. Pchelintsev, A.N., {\em Numerical and physical modeling of the dynamics of the Lorenz system}, Numerical Analysis and Applications, \textbf{7(2)}(2014), 159--167.
  14. Pehlivan, \.{I}., Uyaro\u{g}lu, Y,. {\em A new chaotic attractor from general Lorenz system family and its electronic experimental implementation}, Turk J Elec Eng \& Comp Sci, \textbf{18(2)}(2010), 171--184.
  15. Sermutlu, E., {\em Comparison of Runge-Kutta Methods Order 4 and 5 on Lorenz Equations}, Cankaya University Journal of Arts and Sciences, \textbf{1(1)}(2004).
  16. Mathematics Libretexts, https://math.libretexts.org/Bookshelves/Applied\_Mathematics/Book\%3A\_Introduction\_to\_ the\_Modeling\_and\_Analysis\_of\_ Complex\_Systems\_ (Sayama)/09\%3A\_Chaos/9.04\%3A\_Chaos\_in\_Continuous-Time\_Model, (Access date: 23.09.2019).