Rate of Decay of Stable Periodic Solutions of Duffing Equations

2007/03/27 by Hongbin Chen, Yi Li, Chen, Hongbin +1
Mathematics · #34B15 #34D05 #Advanced Differential Equations and Dynamical Systems #Classical Analysis and ODEs (math.CA) #Differential Equations and Numerical Methods #FOS: Mathematics #Nonlinear Differential Equations Analysis #math.CA #msc:34B15 #msc:34D05

paper · pdf · doi:10.48550/arxiv.math/0703816

Key words: Periodic solution; Stability; Rate of decay

arxiv created 2007/03/27 · openalex publication_date 2007/03/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the second-order equations of Duffing type. Bounds for the derivative of the restoring force are given that ensure the existence and uniqueness of a periodic solution. Furthermore, the stability of the unique periodic solution is analyzed; the sharp rate of exponential decay is determined for a solution that is near to the unique periodic solution.

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