Work

Nonlinear resonance in oscillatory systems with decaying perturbations

Year: 2024

Type: article

Abstract: Time-decaying perturbations of nonlinear oscillatory systems in the plane are considered. It is assumed that the unperturbed systems are non-isochronous and the perturbations oscillate with an asymptotically constant frequency. Resonance effects and long-term asymptotic regimes for solutions are investigated. In particular, the emergence of stable states close to periodic ones is discussed. By combining the averaging technique, stability analysis, and constructing suitable Lyapunov functions, the conditions on perturbations are described that guarantee the existence and stability of the phase-locking regime with a resonant amplitude. The results obtained are applied to the perturbed Duffing oscillator.

Source: Discrete and Continuous Dynamical Systems

DOI: 10.3934/dcds.2024143

Author: Oskar A. Sultanov

Language: English

Topic: Advanced Differential Equations and Dynamical Systems

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4404075361

FWCI: 2.709

Cites: 27

Cited by: 4

Related to: 10