A generalized form of Duffing’s Equation is examined in order to gain insight into the characteristics and properties of chaotic motion. It is shown that variations in the forcing function parameters as well as variations in the system’s initial conditions can lead to a chaotic response. The incidence of chaos is presented in the form of chaos maps and the structure of these maps is discussed. The influence of linear spring force on these maps is also examined. Finally, it is shown that an improper choice of time step can cause spurious results with regard to the existence of chaotic motion.
Tongue BH. Characteristics of Numerical Simulations of Chaotic Systems. ASME. J. Appl. Mech. 1987;54(3):695-699. doi:10.1115/1.3173090.