Bifurcations of autoresonant modes in oscillating systems with combined excitation

Abstract

A mathematical model describing the capture of nonlinear systems into the autoresonance by a combined parametric and external periodic slowly varying perturbation is considered. The autoresonance phenomenon is associated with solutions having an unboundedly growing amplitude and a limited phase mismatch. The paper investigates the behaviour of such solutions when the parameters of the excitation pass through bifurcation values. In particular, the stability of different autoresonant modes is analyzed and the asymptotic approximations of autoresonant solutions on asymptotically long time intervals are proposed by a modified averaging method with using the constructed Lyapunov functions.

arXiv comment23 pages, 17 figures

References in corpus (6)

• Capture into resonance and escape from it in a forced nonlinear pendulum
• Parametric autoresonance
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Cited by in corpus (3)

• Stability and bifurcation phenomena in asymptotically Hamiltonian systems
• Damped perturbations of systems with centre-saddle bifurcation
• Autoresonance in oscillating systems with combined excitation and weak dissipation