A Few Inherent Attributes of Two Dimensional Nonlinear Map

Tarini Kr. Dutta; Jayanta Kr. Das; Anil Kr. Jain

doi:https://doi.org/10.14445/22315373/IJMTT-V13P506

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 13 | Number 1 | Year 2014 | Article Id. IJMTT-V13P506 | DOI : https://doi.org/10.14445/22315373/IJMTT-V13P506

A Few Inherent Attributes of Two Dimensional Nonlinear Map

Tarini Kr. Dutta, Jayanta Kr. Das, Anil Kr. Jain

Citation :

Tarini Kr. Dutta, Jayanta Kr. Das, Anil Kr. Jain, "A Few Inherent Attributes of Two Dimensional Nonlinear Map," International Journal of Mathematics Trends and Technology (IJMTT), vol. 13, no. 1, pp. 34-40, 2014. Crossref, https://doi.org/10.14445/22315373/IJMTT-V13P506

Abstract

Here, we consider a two dimensional nonlinear discrete map to find out a few inherent attributes i.e. fixed points, periodic points, bifurcation values of periods2^n,n=0,1,2,3,4…We use suitable numerical methods and have shown how the period doubling bifurcation points ultimately converge to the Feigenbaum constant. We have calculated Feigenbaum value also. We have further verified our findings with the help of bifurcation diagram & the Lyapunov exponent of the map. Computer software package ‘Mathematica’ and ‘C-program’ are used prudentially to implement numerical algorithms for our purpose.

Keywords

Fixed points, Periodic points, Bifurcation points, Feigenbaum constant, Accumulation Point.

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