2017/02/06 by Oskar A. Sultanov, Sultanov, Oskar
Computer Science · Physics and Astronomy · #34C15 #34D05 #37B25 #37B55 #93D20 #Advanced Fiber Laser Technologies #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Dynamics and Pattern Formation #Nonlinear Photonic Systems
paper · pdf · doi:10.48550/arxiv.1702.01548
openalex publication_date 2017/02/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A mathematical model describing the initial stage of the capture of oscillatory systems into autoresonance under the action of slowly varying pumping is considered. Solutions with an infinitely growing amplitude are associated with the autoresonance phenomenon. Stability of such solutions is of great importance because only stable solutions correspond to physically observable motions. We study the stabilizing problem and we show that the adiabatically varying parametric perturbation with decreasing amplitude in time can stabilize the unstable autoresonant modes.