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

The study of real dynamics has attracted much interest of researchers in the last thirty years due to the fast growing availability of computer software for both simulation and graphics. These computer implementations demonstrate and disclose unexpected and aesthetic patterns, generating a number of predictions that lead to new developments in nonlinear phenomena in dynamical systems such as the phenomenon of chaos. In recent years, chaos theory molds the highest quality research in many fields such as different disciplines of science, engineering and technology [1, 2, 3]. Chaos theory is a combination of theoretical, computational, numerical simulation and computer graphics.