Bifurcation and chaotic behavior of two parameter family of generalized logistic maps

Santanu Nandi

Abstract


The goal in the article is to study the bifurcation and chaotic behavior of the maps ηx(1−x)n over the real domain in the real parameter space, considering η is a positive real parameter which is continuous and n is positive integer. The dynamic properties of the proposed family are not only theoretically analyzed, but also they are analyzed graphically and numerically. The fixed points (real) are simulated theoretically and the periodic points are computed numerically. Furthermore, we discussed the stability of the fixed points as well as periodic points. The plot of the bifurcation of the maps are given by altering the parameters. The presence of chaos in the dynamics of this family is investigated by studying period-doubling phenomena in the bifurcation diagram, and chaotic behavior is been quantified by finding positive Lyapunov exponents.

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Published: 2024-05-21

How to Cite this Article:

Santanu Nandi, Bifurcation and chaotic behavior of two parameter family of generalized logistic maps, Adv. Fixed Point Theory, 14 (2024), Article ID 20

Copyright © 2024 Santanu Nandi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Advances in Fixed Point Theory

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