Chaotic Behavior in the Real Dynamics of a One Parameter Family of Functions

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 x =)1x/(xex ,0 xR \ {1} is considered. The fixed points, periodic points and their nature are investigated for the function f x . Bifurcation is shown to occur in the dynamics of f x . Period doubling, which is a route of chaos in the real dynamics, is also shown to take place in the real dynamics of f x . The orbits of the dynamics of f x are graphically represented by time series graphs. Moreover, the chaotic behavior in the dynamics of f x is found by computing positive Lyapunov exponents