Abstract
The chaotic behavior in the real dynamics of a one parameter family of nonlinear functions is studied in the present paper. For this purpose, the function f_λ(x)=λ=xe^x /( x - 1) λ ＞ 0, x ∈ R {1} is considered. The fixed points, periodic points and their nature are investigated for the function fλ(x) . Bifurcation is shown to occur in the dynamics of fλ(x). Period doubling, which is a route of chaos in the real dynamics, is also shown to take place in the real dynamics of fλ(x). The orbits of the dynamics of fλ(x) are graphically represented by time series graphs. Moreover, the chaotic behavior in the dynamics of fλ(x) is found by computing positive Lyapunov exponents.
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