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

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.