Abstract
A method for controlling nonlinear dynamics and chaos previouslydeveloped by the authors is applied to the classical Duffing oscillator.The method, which consists in choosing the best shape of externalperiodic excitations permitting to avoid the transverse intersection ofthe stable and unstable manifolds of the hilltop saddle, is firstillustrated and then applied by using the Melnikov method foranalytically detecting homoclinic bifurcations. Attention is focused onoptimal excitations with a finite number of superharmonics, because theyare theoretically performant and easy to reproduce. Extensive numericalinvestigations aimed at confirming the theoretical predictions andchecking the effectiveness of the method are performed. In particular,the elimination of the homoclinic tangency and the regularization offractal basins of attraction are numerically verified. The reduction ofthe erosion of the basins of attraction is also investigated in detail,and the paper ends with a study of the effects of control on delayingcross-well chaotic attractors.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
