Autoresonant asymptotics in an oscillating system with weak dissipation

DOI10.1007/s11232-009-0086-3zbMath1205.70016OpenAlexW1967040902MaRDI QIDQ1034498

M. A. Shamsutdinov, Leonid A. Kalyakin

Publication date: 6 November 2009

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11232-009-0086-3

zbMATH Keywords

long-time resonancesmall pumping

Mathematics Subject Classification ID

Nonlinear resonances for nonlinear problems in mechanics (70K30)

Related Items (7)

Lyapunov functions in justification theorems for asymptotics ⋮ Random perturbations of autoresonance in oscillating systems with small dissipation ⋮ Stability of the autoresonance in a dissipative system ⋮ Asymptotics of an autoresonance soliton ⋮ Capture and keeping of a resonance near equilibrium ⋮ Synchronization in a nonisochronous nonautonomous system ⋮ Autoresonance in oscillating systems with combined excitation and weak dissipation

Cites Work

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• Asymptotics at infinity of solutions of equations close to Hamiltonian equations
• The separation of motions in systems with rapidly rotating phase
• Passage through a separatrix in a resonance problem with a slowly-varying parameter
• Captures into resonance and scattering on resonance in dynamics of a charged relativistic particle in magnetic field and electrostatic wave
• Averaging in the autoresonance model
• Asymptotic solutions of nonlinear second order differential equations with variable coefficients
• Boundary of the Basin of Attraction for Weakly Damped Primary Resonance

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