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International Journal of Statistika and Mathematika, ISSN: 2277- 2790 E-ISSN: 2249-8605

Volume 4, Issue 3, 2013 pp 61-64

Research Article

Some Aspects of Dynamical Behavior in a One Dimensional Non Linear Chaotic Map

T. K. Dutta¹, A. Kr. Jain², D. Bhattacharjee³

¹Professor, Department of Mathematics, Gauhati University, Guwahati ,Assam, Pin code- 781014, INDIA.

²Assistant Professor, Department of Mathematics, Barama College,Barama, Assam, Pincode-781346,INDIA.

Academic Editor: Dr. Dase R.K.

In this paper we consider  an inverse  non linear algebraic ecological model with μ as control parameter and a,b are taken as constants. Here we create a suitable C-programming and use Mathematica software to study period doubling route to chaos. Also to find out an universal route from order to chaos through period doubling bifurcations we set up   proper numerical methods to get periodic points and bifurcation points of different period 2ⁿ, where n=0,1,2,3,4,5…..and we successively achieve Feigenbaum Universal  Constant(δ)=4.66920161029…  with the help of bifurcation points calculated numerically. It is also seen that chaotic region takes place beyond accumulation point. We also confirm about chaotic region by getting positive Lyapunov Exponent at some parametric values.