Resonances in asymptotically autonomous systems with a decaying chirped-frequency excitation
DOI10.3934/dcdsb.2022144OpenAlexW3152037358MaRDI QIDQ2099185
Publication date: 23 November 2022
Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2103.15882
stabilityphase-lockinglong-time asymptoticsnon-autonomous systemchirped-frequencydamped perturbation
Forced motions for nonlinear problems in mechanics (70K40) Stability of solutions to ordinary differential equations (34D20) Perturbations of ordinary differential equations (34D10) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Asymptotic properties of solutions to ordinary differential equations (34D05) Nonlinear resonances for nonlinear problems in mechanics (70K30) Nonautonomous smooth dynamical systems (37C60)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Synchronization in a nonisochronous nonautonomous system
- On various averaging methods for a nonlinear oscillator with slow time-dependent potential and a nonconservative perturbation
- Parametric resonance in adiabatic oscillators
- Existence of solutions entering at a singular point of an autonomous system having a formal solution
- Construction of the asymptotics of the solutions of the one-dimensional Schrödinger equation with rapidly oscillating potential
- Bifurcations of asymptotically autonomous differential equations
- The separation of motions in systems with rapidly rotating phase
- Convergence results and a Poincaré-Bendixson trichotomy for asymptotically autonomous differential equations
- Existence of the Moller wave operators for \(V(\tau)={\lambda\sin (\mu r^\alpha )\over r^\beta}\)
- Asymptotically autonomous differential equations in the plane
- Analysis I. Integral presentations asymptotic methods
- Averaging for Hamiltonian systems with one fast phase and small amplitudes
- Absolutely continuous spectra of one-dimensional Schrödinger operators and Jacobi matrices with slowly decreasing potentials
- Bifurcations in asymptotically autonomous Hamiltonian systems under oscillatory perturbations
- Autoresonance in oscillating systems with combined excitation and weak dissipation
- Autoresonance in weakly dissipative Klein-Gordon chains
- On the asymptotic stability for nonlinear oscillators with time-dependent damping
- Stochastic perturbations of stable dynamical systems: trajectory-wise approach
- A class of Schrödinger operators with decaying oscillatory potentials
- Mathematical aspects of classical and celestial mechanics. Transl. from the Russian by E. Khukhro.
- Oscillations and Resonances
- Asymptotic Solutions of Strongly Nonlinear Systems of Differential Equations
- Stability, instability, and bifurcation phenomena in non-autonomous differential equations
- Efficient capture of nonlinear oscillations into resonance
- Asymptotic analysis of autoresonance models
- STABLE AND OSCILLATING MOTIONS IN NONAUTONOMOUS DYNAMICAL SYSTEMS. A GENERALIZATION OF C. L. SIEGEL'S THEOREM TO THE NONAUTONOMOUS CASE
- Asymptotic behaviour and expansions of solutions of an ordinary differential equation
- Damped Perturbations of Systems with Center-Saddle Bifurcation
- Conditions for Phase Locking and Dephasing of Autoresonant Pumping
- On asymptotic stability and instability with respect to a fading stochastic perturbation
- BIFURCATIONS AND CONTINUOUS TRANSITIONS OF ATTRACTORS IN AUTONOMOUS AND NONAUTONOMOUS SYSTEMS
- Justification of an Asymptotic Expansion at Infinity
- The Kuramoto Model on Oriented and Signed Graphs
- Stability and bifurcation phenomena in asymptotically Hamiltonian systems
- Asymptotic solution to the problem of autoresonance: Outer expansion
