Chaotic Dynamics of a Periodically Forced Duffing Oscillator with Cubic Quintic Septic Power Nonlinearities.

In this paper, we investigate the chaotic dynamics of Cubic Quintic Septic Duffing oscillator. The conditions of the system parameters for the existence of fixed points and the stability of the undamped free Cubic Quintic Septic Duffing oscillator are obtained. Multiple scales method is employed to determine the various resonance states of the system through frequency-amplitude response curves. Using linear damping, septic coefficient, excitation amplitude and excitation frequency as control parameters, the bifurcation diagrams are drawn numerically and the results are confirmed using phase space trajectories and their corresponding Poincaré sections. The influence of septic nonlinearity, linear damping and excitation amplitude in controlling the chaotic behavior of the system is also investigated. [ABSTRACT FROM AUTHOR]