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International Journal of Latest Research in Science and Technology

DOI:10.29111/ijlrst   ISRA Impact Factor:3.35

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Analysis of the Chaotic Nature in a Cubic Map

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International Journal of Latest Research in Science and Technology Vol.8 Issue 6, pp 20-27,Year 2019

ANALYSIS OF THE CHAOTIC NATURE IN A CUBIC MAP

Pramila Kumari Prajapati , Premchand Sharma , Sankar Haloi

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Received : 23 November 2019; Accepted : 29 December 2019 ; Published : 31 December 2019

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Article No. 10982
Abstract

In this paper we consider a cubic map ax3 + bx2 + cx + d = 0, where a,b,c and d are parameters. A cubic map is a bimodal map which is an iterated discrete-time dynamical system exhibiting chaotic behavior having infinitely many unstable periodic points. Here we have proved the following: 1) This map exhibits transition to period doubling route and finally leads to a bounded chaotic region that possesses many exciting dynamical properties to be studied . 2) Its periodic doubling bifurcation and the reverse bifurcation are studied for different values of the parameters. 3) An analysis has been carried out by using Lyapunov Exponent and Time Series technique . 4)Feigenbaum Universal Delta along with accumulation point have been calculated in order to establish Feigenbaum universal Properties . 5) Many open problems have been posed

Key Words   
Period doubling Bifurcation, Reverse bifurcation, Lyapunov Exponent, Feigenbaum Delta, Chaos,

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References
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To cite this article

Pramila Kumari Prajapati , Premchand Sharma , Sankar Haloi , " Analysis Of The Chaotic Nature In A Cubic Map ", International Journal of Latest Research in Science and Technology . Vol. 8, Issue 6, pp 20-27 , 2019

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