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On the Convergence of Logistic Map in NOOR Orbit

by Renu Chugh, Mamta Rani, Ashish
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 43 - Number 18
Year of Publication: 2012
Authors: Renu Chugh, Mamta Rani, Ashish
10.5120/6200-8739

Renu Chugh, Mamta Rani, Ashish . On the Convergence of Logistic Map in NOOR Orbit. International Journal of Computer Applications. 43, 18 ( April 2012), 1-4. DOI=10.5120/6200-8739

@article{ 10.5120/6200-8739,
author = { Renu Chugh, Mamta Rani, Ashish },
title = { On the Convergence of Logistic Map in NOOR Orbit },
journal = { International Journal of Computer Applications },
issue_date = { April 2012 },
volume = { 43 },
number = { 18 },
month = { April },
year = { 2012 },
issn = { 0975-8887 },
pages = { 1-4 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume43/number18/6200-8739/ },
doi = { 10.5120/6200-8739 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T20:33:43.046881+05:30
%A Renu Chugh
%A Mamta Rani
%A Ashish
%T On the Convergence of Logistic Map in NOOR Orbit
%J International Journal of Computer Applications
%@ 0975-8887
%V 43
%N 18
%P 1-4
%D 2012
%I Foundation of Computer Science (FCS), NY, USA
Abstract

The logistic map rx(1?x) was given by the Belgian mathematician Pierre Francois Verhulst around 1845 and worked as basic model to study the discrete dynamical system. The behavior of logistic map has been already studied in orbits of one-step, two-step and three-step iterative procedures and it has been established that the logistic map is convergent for larger values of 'r' for two-step and three-step iteration methods. In this paper, an attempt have been made to study the convergence of logistic map in Noor orbit, which is a four-step iterative procedure.

References
  1. M. Aidan, J. G. Keating and D. M. Heffernan, A detailed study of the generation of optically detectable watermarks using the logistic map, Chaos Solitons Fractals (2006)(30)(5), pp. 1088–1097.
  2. M. Ausloos and M. Dirickx, The Logistic Map and the Routeto Chaos: From the beginnings to Modern Applications, Springer Verlag, New York, 2005. Zbl 1085. 37001
  3. R. L. Devaney, A First Course In Chaotic Dynamical Systems: Theory And Experiment, Addison-Wesley, MA, 1992. MR1202237
  4. R. A. Holmgren, A First Course in Discrete Dynamical Systems, Springer-Verlag, New York, 1994. MR1269109
  5. A. Kanso and N. Smaoui, Logistics chaotic maps for binary numbers generations, Chaos Solitons Fractals (2007), doi:10. 1016/j. chaos. 2007. 10. 049.
  6. M. Kumar and M. Rani, An experiment with summability methods in the dynamics of the logistic model, Indian J. Math (2005)(47)(1), pp. 77-89. MR2155130
  7. B. Mi, X. Liao and Y. Chen, A novel chaotic encryption scheme based on arithmetic coding, Chaos Solitons Fractals (2008)(38)(5), pp. 1523–1531.
  8. C. Molina, N. Sampson, W. J. Fitzgerald and M. Niranjan, Geometrical techniques for finding the embedding dimension of time series, Proc. IEEE Signal Processing Society Workshop (1996), p. p. 161-169.
  9. M. S. EL Naschie, Nuclear Spacetime Theories, Superstrings, Monster Group and Applications, Chaos Solitons Fractals(1999)(10)(2-3), pp. 567-580.
  10. M. S. EL Naschie, On the universality class of all universality classes and E-infinity space time physics, Chaos Solitons Fractals(2007)(32)(3), pp. 927-936.
  11. M. S. EL Naschie, Super symmetry, transfinite neural networks, hyperbolic manifolds, quantum gravity and the Higgs, Chaos Solitons Fractals (2004)(22)(5), pp. 999-1006.
  12. M. S. EL Naschie, Topics in the mathematical physics of E-infinity theory, Chaos Solitons Fractals (2006)(30)(3), pp. 656-663.
  13. M. A Noor, New approximation schemes for general variational inequalities, J. Math. Anal. Appl. , 251(2000), 217-229.
  14. L. P. L. de Oliveira and M. Sobottka, Cryptography with chaotic mixing, Chaos Solitons Fractals (2008)(35)(3), pp. 466–471. Zbl 1139. 94005 MR2359835
  15. H. O. Peitgen, H. Jurgens and D. Saupe, Chaos And Fractals: New Frontiers of Science, Springer-Verlag, New York, 2004. MR2031217
  16. M. Rani, Ph. D, Thesis, Iterative procedures in fractal and chaos, Gurukala Kangri Vishwavidyala, Hardwar, 2006.
  17. M. Rani and R. Agarwal, Effect of Noise on Julia sets generated by Logistic map, 978-1-4244-5586-7/10, 2010 IEEE, Vol 2.
  18. M. Rani and S. Goel, An experimental approach to study the logistic map in I-superior orbit, Chaos and Complexity Letters, Vol. 5, Iss. 2 (2011), pp. 1-7.
  19. M. Rani and S. Goel, I-Superior approach to study the stability of logistic map, International conf. on Mec. And Elec. Tech. (ICMT 2010), IEEE.
  20. M. Rani and V. Kumar, A new experimental approach study the stability of logistic maps, J. Indian Acad. Math. (2005)(27)(1), 143-156.
  21. H. Salarieh and A. Alasty, Stabilizing unstable fixed points of chaotic maps via minimum entropy control, Chaos Solitons Fractals(2008)(37)(3), pp. 763–769.
  22. W. Song and J. Meng, Research on logistic mapping and synchronization, Proc. IEEE Intelligent Control and Automation,(1996)(1), p. p. 987-991.
  23. R. Wackerbauer, A. Witt, H. Atmanspacher, J. Kurths and H. Scheingraber, A comparative classification of complexity measures, Chaos Solitons Fractals (1994)(4)(1), pp. 133-173.
  24. H. Yang, X. Liao, K. Wong, W. Zhang and P. Wei, A new cryptosystem based on chaotic map and operations algebric, Chaos Solitons Fractals (2008), doi:10. 1016/j. chaos. 2007. 10. 046.
Index Terms

Computer Science
Information Sciences

Keywords

Logistic Map Picard Orbit Noor Orbit