Stability of parametric autoresonance under random perturbations
Oskar Sultanov
TL;DR
This paper analyzes the stability of parametric autoresonance in nonlinear oscillating systems with dissipation, focusing on how deterministic and random perturbations affect the persistence of energy growth over time.
Contribution
It introduces a mathematical model for autoresonance with dissipation and identifies classes of perturbations that preserve stability over long periods.
Findings
Stability of autoresonance can be maintained under certain deterministic perturbations.
Random perturbations can be tolerated without destroying autoresonance stability.
The model describes conditions for energy growth in nonlinear oscillating systems.
Abstract
A mathematical model describing the initial stage of the capture into the parametric autoresonance in nonlinear oscillating systems with a dissipation is considered. Solutions with unboundedly growing energy in time at infinity are associated with the autoresonance phenomenon. Stability of such solutions is investigated. We describe classes of admissible deterministic and random perturbations such that the stability of autoresonance is preserved on an asymptotically large interval.
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Taxonomy
TopicsQuantum chaos and dynamical systems · Nonlinear Dynamics and Pattern Formation · Nonlinear Photonic Systems