Stability and Asymptotic Analysis of the Autoresonant Capture in Oscillating Systems with Combined Excitation

DOI10.1137/18M1194250zbMath1411.34053arXiv1804.08372MaRDI QIDQ4555743

O. A. Sultanov

Publication date: 21 November 2018

Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1804.08372

zbMATH Keywords

stabilityLyapunov functionnonlinear oscillationsasymptoticaveraging methodautoresonance

Mathematics Subject Classification ID

Stability of solutions to ordinary differential equations (34D20) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Averaging method for ordinary differential equations (34C29) Asymptotic properties of solutions to ordinary differential equations (34D05) Asymptotic expansions of solutions to ordinary differential equations (34E05) Topological dynamics of nonautonomous systems (37B55)

Related Items (4)

Decaying oscillatory perturbations of Hamiltonian systems in the plane ⋮ Damped Perturbations of Systems with Center-Saddle Bifurcation ⋮ Stability and bifurcation phenomena in asymptotically Hamiltonian systems ⋮ Autoresonance in oscillating systems with combined excitation and weak dissipation

Cites Work

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• Stability of autoresonance models
• Existence of solutions entering at a singular point of an autonomous system having a formal solution
• The capture into parametric autoresonance
• Existence theorems and estimates of solutions for equations of principal resonance
• Stability of capture into parametric autoresonance
• Mathematical aspects of classical and celestial mechanics. Transl. from the Russian by E. Khukhro.
• Asymptotic behavior of solutions of equations of main resonance
• Asymptotic Solutions of Strongly Nonlinear Systems of Differential Equations
• Efficient capture of nonlinear oscillations into resonance
• Asymptotic analysis of autoresonance models
• Justification of an Asymptotic Expansion at Infinity

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