Chaotic Dynamics of an Extended Duffing Oscillator Under Periodic Excitation

In this paper, chaotic dynamics of a cubic-quintic-septic Duffing oscillator subjected to periodic excitation is investigated. The multiple scales method is used to determine the various resonance states of the model. It is found that the considered model posses thirteen resonance states whose seven are thoroughly studied. The steady-state solutions and theirs stabilities are determined. The frequency-amplitude curves show that the considered system presents mixed behavior, limit cycles, hysteresis, jump and bifurcation phenomena. It is also noticed that these phenomena are strongly influenced by quintic-septic nonlinearity and excitation amplitude. Bifurcation structures displayed by the model for each considered type of resonant states are investigated numerically using the fourth-order Runge-Kutta algorithm. As results, the quintic-septic nonlinearity, linear dissipation and excitation amplitude can be used to control the chaotic behavior of the system.