Bin the Case Bifurcation and Chaos of Logistic Maps with Three Parameters and its Applications

Authors:

Asia Ali Mohammed,Assistant Prof. Radhi A. Zaboon,

DOI NO:

https://doi.org/10.26782/jmcms.2019.06.00045

Keywords:

fixed point ,stability,bin the case bifurcation diagram,periodic point,

Abstract

In this paper, the generalization of logistic discrete dynamic systems with three parameters have been analyzed with the necessary mathematical requirements and proofs. The dynamics and the qualitative properties of the fixed points and their stability, the bin the case bifurcation diagram and chaos have proposed with application.

Refference:

I.A. Ferrettia, N. K. Rahman , “A study of Coupled Logistic Map and Its Applications in Chemical Pysics” , Chemical Pysics,vol.119 , no.2-3, pp: 275-288,1988.
II.C.Robiason, “Dynamical System. Stability , Symbolic Dynamics and Chaos “, second edition ,CRC Press Boca Ration.Florida,1999.
III.C. Pellicer –Lostao , R. Lpez – Ruiz,”A Chaotic gas- like Model for Trading Markets “,Journal of Computational Science,vol.1, no.1, pp: 24- 32,2010.
IV.D.Gulick, ” Encounters with Chaos “, McGraw Hill, 1990.
V.F .G. Alvarez, Monotoya, G. Pastor, and M. Romera,” Chaotic cryptosystems”, In Proceedings of IEEE International Carnahan Conference on Security Technology, pp: 332-338, 1999.
VI.G.Geoffrey . ,”Chaotic Dynamics; Fractals, Tilings and Substitutions”,Towson University Mathematics Department, 2015.
VII.G. Jakimoski, and L. Kocarev, “Chaos and cryptography: Block encryption ciphers based on chaotic maps “, IEEE Transactionson Circuits and Systems-I: Fundamental Theory and Applications, vol. 48, no.2,
pp:163-169, 2001.
VIII.G. R.Ahmed ,”On Some Generalized Discrete Logistic Maps” , Journal of Advance Research , vol.4, no.2, pp:163-171,2013.
IX.H. R.Biswas, “One Dimensional Chaotic Dynamical Systems “, Journal of Pure and Applied Mathematics :Advance andApplications , Vol. 10, no.0, pp: 69-101, 2013.
X.I.Sajid ,R.Muhammad ,I.Shahaid ,O.Muhammad , A. S.Hadeed,”Study of Nonlinear Dynamics Using Logistic Map”, LUMS 2nd International Conference on Mathematics and its Applications in Information Technology (LICM08), 2008.
XI.K. Pareeka .N.VinodPatidara ,K . K. Sud ,” Image Encryption Using Chaotic Logistic Map ” ,Image and Vision Computing , vol. 24, no.9, pp: 926-934,2006.
XII.M. SBaptista, ” Cryptography with chaos”, Physics Letters A. Vol. 240, no.1-2, pp: 50-54, 1998.
XIII.R.Klages ,” Applied Dynamical System”, Lectures 5-10 From Deterministic Chaos to Deterministic Din the case offusion, Rainer Klages, QMUL,2010
XIV.R.A.J.Matthews ” On the Derivation of a Chaotic Encryption Algorithm”. Cryptologia, vol.13, no.1, pp: 29-42, 1989.
XV.R. L. Devaney, L. Keen ,”Chaos and Fractals :The Mathematics Behind The Computer Graphics “, American Mathematical Society ,Providence, 1989.
XVI.R. Rak, E. Rak ,” Route to Chaos in Generalized Logistic Map” , Faculty of Mathematics and Natural Science ,University of Rezesow , PL-35-45, Rezesow ,Poland ,2015.
XVII.S. Sternberg. “The Perron-Frobenius Theorem”, Dynamical Systems, pp: 175-195, 2011.
XVIII.T. Habutsu, Y. Nishio, I. Sasase, and S. Mori, “A secret key cryptosystem by iterating a chaotic map”, Advances in Cryptology:Proceedings of EUROCRYPT 91, LNCS 547, Berlin:Springer-Verlag, pp: 127-140, 1991.
XIX.T. –Y. Li and J .York ” Period Three Implies Chaos ” , American Mathematical Monthly, vol.82, no.10, pp: 985-992,1975.
XX.W .Xiangjun ,Haibin K. , Jürgen K. , ” A New Color Image Encryption Scheme Based on DNA Sequences and Multiple Improved 1D Chaotic Maps ” , Contents lists available at Science Direct Applied Soft
Computing journal homepage : www.elsevier.com/locate/asoc,2015.
XXI.Z. Kotulski, and J. Szczepanski, ” Discrete chaotic cryptography”, Annalen der Physik, vol. 509, no.5, pp: 381-394, 1997.
XXII.Z. L. Zhou ,” Symbolic Dynamics (chinsi)” , Shanghai Scientin the case ofic and Technology Education Publish House Shanghai, 1997.
Asia Ali Mohammed, Assistant Prof. Radhi A. Zaboon View Download