Periodic Solution and Stability Behavior for Nonlinear Oscillator Having a Cubic Nonlinearity Time-Delayed

Yusry Osman El-Dib
2018 International Annals of Science  
The current paper investigates the dynamics of the dissipative system with a cubic nonlinear time-delayed of the type of the damping Duffing equation. A coupling between the method of the multiple scales and the homotopy perturbation has been utilized to study the complicated dynamic problem. Through this approach, a cubic nonlinear amplitude equation resulted in at the first-order of perturbation; meanwhile, a quintic equation appears at the second-order of perturbation. These equations are
more » ... bined into one nonlinear quintic Landau equation. The polar form solution is used, and linearized stability configuration is applied to the nonlinear amplitude equation. Also, a second-order approximate solution is achieved. The numerical illustrations showed that the damping, delay coefficient, and time delay play dual roles in the stability behavior. In addition, the nonlinear coefficient plays a destabilizing influence.
doi:10.21467/ias.5.1.12-25 fatcat:sfddd55iaza3vhtdouqhkjdmsa