Abstract
We use the residue harmonic balance scheme to study the periodic motions of a class of second-order delay-differential equations with cubic nonlinearities near and after Hopf bifurcation. The multiple solutions are found by homotopy continuation. Then, the approximation to any desired accuracy for a specific solution is captured by solving linear equations iteratively. The second-order solutions give good predictions for the frequency and amplitude, which are verified by the Runge–Kutta numerical solutions. Two typical examples, the temporal dynamics of the delay Liénard oscillator and the delay feedback Duffing system, are studied and compared. The results show how to trace analytically the relevant effect of the stiffness coefficient and the time delay on the dynamics and on the number of periodic solutions, even for large values of the bifurcation parameters.
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.
