Asymptotic analysis of autoresonance models
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Publication:3613121
DOI10.1070/RM2008v063n05ABEH004560zbMath1159.70015OpenAlexW2068832873MaRDI QIDQ3613121
Publication date: 11 March 2009
Published in: Russian Mathematical Surveys (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1070/rm2008v063n05abeh004560
General perturbation schemes for nonlinear problems in mechanics (70K60) Nonlinear resonances for nonlinear problems in mechanics (70K30) Research exposition (monographs, survey articles) pertaining to mechanics of particles and systems (70-02) Averaging of perturbations for nonlinear problems in mechanics (70K65)
Related Items (33)
Asymptotic analysis of the model of gyromagnetic autoresonance ⋮ Lyapunov functions in justification theorems for asymptotics ⋮ Stability of the autoresonance in a dissipative system ⋮ WKB method for nonlinear equations of Emden-Fowler type ⋮ Asymptotic behaviour of measure for captured trajectories into parametric autoresonance ⋮ Stability and Asymptotic Analysis of the Autoresonant Capture in Oscillating Systems with Combined Excitation ⋮ Asymptotics of an autoresonance soliton ⋮ Stability of equilibrium with respect to white noise ⋮ Stability of capture into parametric autoresonance ⋮ Stability of autoresonance models ⋮ Adiabatic approximation for a model of cyclotron motion ⋮ Stability of autoresonance models subject to random perturbations for systems of nonlinear oscillation equations ⋮ Random perturbations of parametric autoresonance ⋮ Long-Term Behaviour of Asymptotically Autonomous Hamiltonian Systems with Multiplicative Noise ⋮ Painlevé II equation as a model of a resonant interaction of oscillators ⋮ Capture and keeping of a resonance near equilibrium ⋮ Conditions for Phase Locking and Dephasing of Autoresonant Pumping ⋮ Capture into parametric autoresonance in the presence of noise ⋮ Autoresonance excitation of a soliton of the nonlinear Schrödinger equation ⋮ Adiabatic approximation in a resonance capture problem ⋮ Capture and holding of resonance far from equilibrium ⋮ On the frequency of a nonlinear oscillator ⋮ Lyapunov functions and asymptotics at infinity of solutions of equations that are close to Hamiltonian equations ⋮ Synchronization in a nonisochronous nonautonomous system ⋮ Existence theorems and estimates of solutions for equations of principal resonance ⋮ Scattering of trajectories at a separatrix under autoresonance ⋮ Resonance capture in a system of two oscillators near equilibrium ⋮ On a cascade of autoresonances in an elevator cable system ⋮ Bifurcations in asymptotically autonomous Hamiltonian systems under oscillatory perturbations ⋮ Damped Perturbations of Systems with Center-Saddle Bifurcation ⋮ Resonances in asymptotically autonomous systems with a decaying chirped-frequency excitation ⋮ Lyapunov functions in barriers for parabolic equations and in stability problems with respect to ``white noise ⋮ Autoresonance in oscillating systems with combined excitation and weak dissipation
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