Autoresonance in oscillating systems with combined excitation and weak dissipation
arXiv:2009.08254 · doi:10.1016/j.physd.2020.132835
Abstract
A mathematical model describing the initial stage of the capture into autoresonance for nonlinear oscillating systems with combined parametric and external excitation is considered. The solutions with unboundedly growing amplitude and limited phase mismatch correspond to the autoresonant capture. The paper investigates the existence, stability and bifurcations of such solutions in the presence of a weak dissipation in the system. Our technique is based on the study of particular solutions with power-law asymptotics at infinity and the construction of suitable Lyapunov functions.
arXiv comment18 pages, 8 figures. arXiv admin note: substantial text overlap with arXiv:1907.07482
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- Damped perturbations of systems with centre-saddle bifurcation
- Bifurcations in asymptotically autonomous Hamiltonian systems under multiplicative noise
- Resonances in asymptotically autonomous systems with a decaying chirped-frequency excitation
- Long-term behaviour of asymptotically autonomous Hamiltonian systems with multiplicative noise