Dynamical integrity of the safe basins in a problem of forced escape

2024/01/23 by Kravetc, Pavel, Gendelman, Oleg, Fidlin, Alexander
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2401.13091

Abstract

This paper explores the use of the Approximation of Isolated Resonance (AIR) method for determining the safe basins (SBs) in the problem of escape from a potential well. The study introduces a novel approach to capture the location and the shape of the SBs and establish their erosion profiles. The research highlights the concept of "true" safe basins, which remain invariant with phase shifts, a critical factor often faced in real-world applications. A cubic polynomial potential serves as the benchmark to illustrate the proposed method.

Related

• Analytic exploration of safe basins in a benchmark problem of forced escape
• Basic mechanisms of escape of a harmonically forced classical particle from a potential well
• Escape dynamics of a particle from a purely-nonlinear truncated quartic potential well under harmonic excitation
• Escape from a potential well under forcing and damping with application to ship capsize
• Escape of a forced-damped particle from weakly nonlinear truncated potential well