On the Convergence of Logistic Map in NOOR Orbit

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.

[1]  A. Levine,et al.  New estimates of the storage permanence and ocean co-benefits of enhanced rock weathering , 2023, PNAS nexus.

[2]  Mamta Rani,et al.  I-superior approach to study the stability of logistic map , 2010, 2010 International Conference on Mechanical and Electrical Technology.

[3]  J. Kurths,et al.  A Comparative Classification of Complexity Measures , 1994 .

[4]  M. Noor.  New approximation schemes for general variational inequalities , 2000 .

[5]  Robert L. Devaney,et al.  A First Course In Chaotic Dynamical Systems: Theory And Experiment , 1993 .

[6]  Richard A. Holmgren.  A First Course in Discrete Dynamical Systems , 1994 .

[7]  M. E. Naschie,et al.  Nuclear Spacetime Theories, Superstrings, MonsterGroup and Applications , 1999 .

[8]  M. E. Naschie,et al.  On the universality class of all universality classes and E-infinity spacetime physics , 2007 .

[9]  L. P. L. D. Oliveira,et al.  Cryptography with chaotic mixing , 2008 .

[10]  John G. Keating,et al.  A detailed study of the generation of optically detectable watermarks using the logistic map , 2006 .

[11]  M. E. Naschie,et al.  Supersymmetry, transfinite neural networks, hyperbolic manifolds, quantum gravity and the Higgs , 2004 .

[12]  Wei Song,et al.  Research on Logistic Mapping and Synchronization , 2006, 2006 6th World Congress on Intelligent Control and Automation.

[13]  M. S. El Naschie,et al.  Topics in the mathematical physics of E-infinity theory , 2006 .

[14]  Aria Alasty,et al.  Stabilizing unstable fixed points of chaotic maps via minimum entropy control , 2008 .

[15]  A. Kanso,et al.  Logistic chaotic maps for binary numbers generations , 2009 .

[16]  X. Liao,et al.  A novel chaotic encryption scheme based on arithmetic coding , 2008 .

[17]  Marcel Ausloos,et al.  The logistic map and the route to chaos : from the beginnings to modern applications , 2006 .

[18]  Peter Rodgers.  Super symmetry , 2008 .

[19]  Dietmar Saupe,et al.  Chaos and fractals - new frontiers of science , 1992 .

[20]  M. Niranjan,et al.  Geometrical techniques for finding the embedding dimension of time series , 1996, Neural Networks for Signal Processing VI. Proceedings of the 1996 IEEE Signal Processing Society Workshop.

[21]  Kwok-Wo Wong,et al.  A new cryptosystem based on chaotic map and operations algebraic , 2009 .