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Stability and Fractal Patterns of Complex Logistic Map

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Nov 05, 2014

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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.Search in Google Scholar

2. Barnsley, M. F. Superfractals. Cambridge, Cambridge University Press, 2006.10.1017/CBO9781107590168Search in Google Scholar

3. A. Bunde, S. Havlin, Eds. Fractals in Science. Springer-Verlag, 1994.10.1007/978-3-642-77953-4Search in Google Scholar

4. Camacho, E. F., C. Bordons. Model Predictive Control. Berlin, Springer, 1999.10.1007/978-1-4471-3398-8Search in Google Scholar

5. Crownover, R. M. Introduction to Fractals and Chaos. Jones & Barlett Publishers, 1995.Search in Google Scholar

6. Dettmer, R. Chaos and Engineering. - IEE Review, September 1993, 199-203.10.1049/ir:19930095Search in Google Scholar

7. Devaney, R. L. A First Course in Chaotic Dynamical Systems: Theory and Experiment.Addison-Wesley, 1992.Search in Google Scholar

8. Feigenbaum, M. Quantitative Universality for a Class of Non-Linear Transformations. - J. Statistical Physics, Vol. 19, 1978, 25-52.10.1007/BF01020332Search in Google Scholar

9. Holmgren, R. A. A First Course in Discrete Dynamical Systems. Springer-Verlag, 1994.10.1007/978-1-4684-0222-3Search in Google Scholar

10. Ishikawa, S. Fixed Points by a New Iteration Method. - Proc. Amer. Math. Soc., Vol. 44, 1974, No 1, 147-150.10.1090/S0002-9939-1974-0336469-5Search in Google Scholar

11. Julien, C. S. Chaos and Time-Series Analysis. Oxford University Press, 2003.Search in Google Scholar

12. Keller, K. Invariant Factors, Julia Equivalences, and the (Abstract) Mandelbrot Set. - Berlin Heidelberg New York, Springer-Verlag, 2000.10.1007/BFb0103999Search in Google Scholar

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.Search in Google Scholar

14. Mann, W. R. Mean Value Methods in Iteration. - Proc. Amer. Math. Soc., Vol. 4, 1953, No 3, 506-510.10.1090/S0002-9939-1953-0054846-3Search in Google Scholar

15. May, R. M. Simple Mathematical Models with Very Complicated Dynamics. - Nature, Vol. 261 1976, No 459, 459-475.10.1038/261459a0934280Search in Google Scholar

16. May, R. M., G. F. Oster. Bifurcations and Dynamic Complexity in Simple Biological Models. - The American Naturalist, Vol. 110, 1976, No 974, 573-599.10.1086/283092Search in Google Scholar

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, 1088-1097.10.1016/j.chaos.2005.09.029Search in Google Scholar

18. Moran, P. A. P. Some Remarks on Animal Population Dynamics. - Biometrics, Vol. 6, 1950, No 3, 250-258.10.2307/3001822Search in Google Scholar

19. Pareek, N. K., V. Patidar, K. K. Sud. Image Encryption Using Chaotic Logistic Map. - Image and Vision Computing, Vol. 24, 2006, No 9, 926-934.10.1016/j.imavis.2006.02.021Search in Google Scholar

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.Search in Google Scholar

21. Peitgen, H., H. Jurgens, D. Saupe. Chaos and Fractals: New Frontiers of Science.Springer-Verlag, 2004.10.1007/b97624Search in Google Scholar

22. H. Peitgen, D. Saupe, Eds. The Science of Fractal Images. Springer-Verlag, 1988.Search in Google Scholar

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.Search in Google Scholar

24. Prasad, B., K. Katiyar. Fractals via Ishikawa Iteration. - CCIS, Springer, Berlin, Heidelberg, Vol. 140, 2011, No 2, 197-203.10.1007/978-3-642-19263-0_24Search in Google Scholar

25. Prasad, B., K. Katiyar. A Stability Analysis of Logistic Model. - International Journal of Nonlinear Science, Vol. 17, 2014, No 1, 71-79.Search in Google Scholar

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, 2062-2066.10.1016/j.chaos.2008.08.022Search in Google Scholar

27. Rani, M., R. Agarwal. Generation of Fractals from Complex Logistic Map. - Chaos, Solitons and Fractals, Vol. 42, 2009, No 1, 447-452.10.1016/j.chaos.2009.01.011Search in Google Scholar

28. Salarieh, H., M. Shahrokhi. Indirect Adaptive Control of Discrete Chaotic Systems. - Chaos, Solitons and Fractals, Vol. 34, 2007, No 4, 1188-1201.10.1016/j.chaos.2006.03.115Search in Google Scholar

Language:
English
Publication timeframe:
4 times per year
Journal Subjects:
Computer Sciences, Information Technology