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A Modified Quadratic Lorenz Attractor in Geometric Multiplicative Calculus

Year 2023, Volume: 15 Issue: 2, 407 - 413, 31.12.2023

Bugce Eminaga Tatlicioglu

https://doi.org/10.47000/tjmcs.1249554

Abstract

In this study the modified quadratic Lorenz attractor is introduced in geometric multiplicative calculus. The
new system is analyzed and discussed for the chaotic behaviour in detail. The equilibria points, the eigenvalues of the multiplicative Jacobian, and the Lyapunov exponents are determined. The numerical simulations are conducted using the Runge-Kutta method in the framework of geometric multiplicative calculus highlighting the chaotic behaviour.

Keywords

Chaos dynamical system multiplicative calculus

References

  • Aniszewska, D., Multiplicative runge–kutta methods, Nonlinear Dynamics, 50(1)(2007), 265–272.
  • Aniszewska, D., Rybaczuk, M., Lyapunov type stability and Lyapunov exponent for exemplary multiplicative dynamical systems, Nonlinear Dynamics, 54(4)(2008), 345–354.
  • Chen, G., Ueta, T., Yet another chaotic attractor, International Journal of Bifurcation and Chaos, 9(07)(1999), 1465–1466.
  • Eminağa, B., Aktöre, H., Riza, M. A modified quadratic Lorenz attractor, ArXiv e-prints 1508.06840 (Aug. 2015).
  • Holmes, P., Poincar´e, celestial mechanics, dynamical-systems theory and chaos, Physics Reports, 193(3)(1990), 137–163.
  • Lorenz, E.N., Deterministic nonperiodic flow, Journal of the Atmospheric Sciences, 20(2)(1963), 130–141.
  • Lu, J., Chen, G., A new chaotic attractor coined, International Journal of Bifurcation and Chaos, 12(03)(2002), 659–661.
  • Lu, J.G., Chaotic dynamics of the fractional-order Lu system and its synchronization, Physics Letters A, 354(4)(2006), 305–311.
  • Lyapunov, A.M., The general problem of the stability of motion, International Journal of Control, 55(3)(1992), 531–534.
  • Ott, E., Chaos in Dynamical Systems, Cambridge University Press, 2002.
  • Pehlivan, I., Uyaroglu, Y., A new chaotic attractor from general lorenz system family and its electronic experimental implementation, Turkish Journal of Electrical Engineering and Computer Sciences, 18(2)(2010), 171–184.
  • Poincare, H., Lectures on Celestial Mechanics, 1965.
  • Poincare, H., New Methods of Celestial Mechanics, History of Modern Physics and Astronomy, New York: American Institute of Physics 156 (AIP),— c1993 1, 1993.
  • Riza, M., Aktöre, H., The runge–kutta method in geometric multiplicative calculus, LMS Journal of Computation and Mathematics, 15818(2015), 539–554.
  • Rössler, O., An equation for continuous chaos, Physics Letters A, 57(5)(1976), 397–398.

Year 2023, Volume: 15 Issue: 2, 407 - 413, 31.12.2023

Bugce Eminaga Tatlicioglu

https://doi.org/10.47000/tjmcs.1249554

Abstract

References

  • Aniszewska, D., Multiplicative runge–kutta methods, Nonlinear Dynamics, 50(1)(2007), 265–272.
  • Aniszewska, D., Rybaczuk, M., Lyapunov type stability and Lyapunov exponent for exemplary multiplicative dynamical systems, Nonlinear Dynamics, 54(4)(2008), 345–354.
  • Chen, G., Ueta, T., Yet another chaotic attractor, International Journal of Bifurcation and Chaos, 9(07)(1999), 1465–1466.
  • Eminağa, B., Aktöre, H., Riza, M. A modified quadratic Lorenz attractor, ArXiv e-prints 1508.06840 (Aug. 2015).
  • Holmes, P., Poincar´e, celestial mechanics, dynamical-systems theory and chaos, Physics Reports, 193(3)(1990), 137–163.
  • Lorenz, E.N., Deterministic nonperiodic flow, Journal of the Atmospheric Sciences, 20(2)(1963), 130–141.
  • Lu, J., Chen, G., A new chaotic attractor coined, International Journal of Bifurcation and Chaos, 12(03)(2002), 659–661.
  • Lu, J.G., Chaotic dynamics of the fractional-order Lu system and its synchronization, Physics Letters A, 354(4)(2006), 305–311.
  • Lyapunov, A.M., The general problem of the stability of motion, International Journal of Control, 55(3)(1992), 531–534.
  • Ott, E., Chaos in Dynamical Systems, Cambridge University Press, 2002.
  • Pehlivan, I., Uyaroglu, Y., A new chaotic attractor from general lorenz system family and its electronic experimental implementation, Turkish Journal of Electrical Engineering and Computer Sciences, 18(2)(2010), 171–184.
  • Poincare, H., Lectures on Celestial Mechanics, 1965.
  • Poincare, H., New Methods of Celestial Mechanics, History of Modern Physics and Astronomy, New York: American Institute of Physics 156 (AIP),— c1993 1, 1993.
  • Riza, M., Aktöre, H., The runge–kutta method in geometric multiplicative calculus, LMS Journal of Computation and Mathematics, 15818(2015), 539–554.
  • Rössler, O., An equation for continuous chaos, Physics Letters A, 57(5)(1976), 397–398.
There are 15 citations in total.

Details

Primary Language English
Subjects Software Engineering (Other)
Journal Section Articles
Authors

Bugce Eminaga Tatlicioglu 0000-0001-8854-4464

Publication Date December 31, 2023
Published in Issue Year 2023 Volume: 15 Issue: 2

Cite

APA Eminaga Tatlicioglu, B. (2023). A Modified Quadratic Lorenz Attractor in Geometric Multiplicative Calculus. Turkish Journal of Mathematics and Computer Science, 15(2), 407-413. https://doi.org/10.47000/tjmcs.1249554
AMA Eminaga Tatlicioglu B. A Modified Quadratic Lorenz Attractor in Geometric Multiplicative Calculus. TJMCS. December 2023;15(2):407-413. doi:10.47000/tjmcs.1249554
Chicago Eminaga Tatlicioglu, Bugce. “A Modified Quadratic Lorenz Attractor in Geometric Multiplicative Calculus”. Turkish Journal of Mathematics and Computer Science 15, no. 2 (December 2023): 407-13. https://doi.org/10.47000/tjmcs.1249554.
EndNote Eminaga Tatlicioglu B (December 1, 2023) A Modified Quadratic Lorenz Attractor in Geometric Multiplicative Calculus. Turkish Journal of Mathematics and Computer Science 15 2 407–413.
IEEE B. Eminaga Tatlicioglu, “A Modified Quadratic Lorenz Attractor in Geometric Multiplicative Calculus”, TJMCS, vol. 15, no. 2, pp. 407–413, 2023, doi: 10.47000/tjmcs.1249554.
ISNAD Eminaga Tatlicioglu, Bugce. “A Modified Quadratic Lorenz Attractor in Geometric Multiplicative Calculus”. Turkish Journal of Mathematics and Computer Science 15/2 (December 2023), 407-413. https://doi.org/10.47000/tjmcs.1249554.
JAMA Eminaga Tatlicioglu B. A Modified Quadratic Lorenz Attractor in Geometric Multiplicative Calculus. TJMCS. 2023;15:407–413.
MLA Eminaga Tatlicioglu, Bugce. “A Modified Quadratic Lorenz Attractor in Geometric Multiplicative Calculus”. Turkish Journal of Mathematics and Computer Science, vol. 15, no. 2, 2023, pp. 407-13, doi:10.47000/tjmcs.1249554.
Vancouver Eminaga Tatlicioglu B. A Modified Quadratic Lorenz Attractor in Geometric Multiplicative Calculus. TJMCS. 2023;15(2):407-13.