Abstract: In this paper, we highlight three objectives on a
nonlinear fifth degree chaotic unimodal map given by in which is a suitable parameter. Firstly, we
establish the Feigenbaum tree of bifurcation points leading to a chaotic region;
secondly, the graphs of the time series analysis are demonstrated in order to
support our periodic orbits of periods and thirdly, we calculate Lyapunov
exponents for confirmation of the existence of the chaotic region. These results
have opened up further research work in other chaotic models of this kind.
Keywords and phrases: Feigenbaum tree, bifurcation points, time series graphs, Lyapunov exponents.
