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Stability and Fractal Patterns of Complex Logistic Map Cover

Stability and Fractal Patterns of Complex Logistic Map

Open Access
|Nov 2014

References

  1. 1. Barnsley, M. F. Fractals Everywhere. Second Ed. Revised with the Assistance of and a Foreword by Hawley Rising, III. Boston MA, Academic Press Professional, 1993.
  2. 2. Barnsley, M. F. Superfractals. Cambridge, Cambridge University Press, 2006.
  3. 3. A. Bunde, S. Havlin, Eds. Fractals in Science. Springer-Verlag, 1994.
  4. 4. Camacho, E. F., C. Bordons. Model Predictive Control. Berlin, Springer, 1999.
  5. 5. Crownover, R. M. Introduction to Fractals and Chaos. Jones & Barlett Publishers, 1995.
  6. 6. Dettmer, R. Chaos and Engineering. - IEE Review, September 1993, 199-203.
  7. 7. Devaney, R. L. A First Course in Chaotic Dynamical Systems: Theory and Experiment.Addison-Wesley, 1992.
  8. 8. Feigenbaum, M. Quantitative Universality for a Class of Non-Linear Transformations. - J. Statistical Physics, Vol. 19, 1978, 25-52.
  9. 9. Holmgren, R. A. A First Course in Discrete Dynamical Systems. Springer-Verlag, 1994.
  10. 10. Ishikawa, S. Fixed Points by a New Iteration Method. - Proc. Amer. Math. Soc., Vol. 44, 1974, No 1, 147-150.
  11. 11. Julien, C. S. Chaos and Time-Series Analysis. Oxford University Press, 2003.
  12. 12. Keller, K. Invariant Factors, Julia Equivalences, and the (Abstract) Mandelbrot Set. - Berlin Heidelberg New York, Springer-Verlag, 2000.
  13. 13. Kint, J., D. Constales, A. Vanderbauwhede. Pierre-Francois Verhulst’s Final Triumph. - In: M. Ausloos, M. Dirickx Eds. The Logistic Map and the Route to Chaos: From the Beginnings to Modern Applications. Springer-Verlag, 2006.
  14. 14. Mann, W. R. Mean Value Methods in Iteration. - Proc. Amer. Math. Soc., Vol. 4, 1953, No 3, 506-510.
  15. 15. May, R. M. Simple Mathematical Models with Very Complicated Dynamics. - Nature, Vol. 261 1976, No 459, 459-475.
  16. 16. May, R. M., G. F. Oster. Bifurcations and Dynamic Complexity in Simple Biological Models. - The American Naturalist, Vol. 110, 1976, No 974, 573-599.
  17. 17. Mooney, A., J. G. Keating, D. M. Heffernan. A Detailed Study of the Generation of Optically Detectable Watermarks Using the Logistic Map. - Chaos, Solitons and Fractals, Vol. 30, 2006, No 5, 1088-1097.
  18. 18. Moran, P. A. P. Some Remarks on Animal Population Dynamics. - Biometrics, Vol. 6, 1950, No 3, 250-258.
  19. 19. Pareek, N. K., V. Patidar, K. K. Sud. Image Encryption Using Chaotic Logistic Map. - Image and Vision Computing, Vol. 24, 2006, No 9, 926-934.
  20. 20. Pastijn, H. Chaotic Growth with the Logistic Model of P.-F. Verhulst. - In: M. Ausloos, M. Dirickx, Eds. The Logistic Map and the Route To Chaos: From the Beginnings to Modern Applications. - Springer-Verlag, 2006.
  21. 21. Peitgen, H., H. Jurgens, D. Saupe. Chaos and Fractals: New Frontiers of Science.Springer-Verlag, 2004.
  22. 22. H. Peitgen, D. Saupe, Eds. The Science of Fractal Images. Springer-Verlag, 1988.
  23. 23. Prasad, B., K. Katiyar. A Comparative Study of Logistic Map Through Function Iteration. - In: Proc. Int. Con. Emerging Trends in Engineering and Technology. ISBN: 978-93-80697-22-2, Kurukshetra, India, 2010, 357-359.
  24. 24. Prasad, B., K. Katiyar. Fractals via Ishikawa Iteration. - CCIS, Springer, Berlin, Heidelberg, Vol. 140, 2011, No 2, 197-203.
  25. 25. Prasad, B., K. Katiyar. A Stability Analysis of Logistic Model. - International Journal of Nonlinear Science, Vol. 17, 2014, No 1, 71-79.
  26. 26. Rani, M., R. Agarwal. A New Experimental Approach to Study the Stability of Logistic Map. - Chaos, Solitons and Fractals, Vol. 41, 2009, No 4, 2062-2066.
  27. 27. Rani, M., R. Agarwal. Generation of Fractals from Complex Logistic Map. - Chaos, Solitons and Fractals, Vol. 42, 2009, No 1, 447-452.
  28. 28. Salarieh, H., M. Shahrokhi. Indirect Adaptive Control of Discrete Chaotic Systems. - Chaos, Solitons and Fractals, Vol. 34, 2007, No 4, 1188-1201.
DOI: https://doi.org/10.2478/cait-2014-0029 | Journal eISSN: 1314-4081 | Journal ISSN: 1311-9702 (formerly 1314-4081)
Language: English
Page range: 14 - 24
Published on: Nov 5, 2014
Published by: Bulgarian Academy of Sciences, Institute of Information and Communication Technologies
In partnership with: Paradigm Publishing Services

© 2014 Bhagwati Prasad, Kuldip Katiyar, published by Bulgarian Academy of Sciences, Institute of Information and Communication Technologies
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.