The Lyapunov Stability for the Linear and Nonlinear Damped Oscillator with Time-Periodic Parameters
| Autor: | Jifeng Chu, Ting Xia |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2010 |
| Předmět: | |
| Zdroj: | Abstract and Applied Analysis, Vol 2010 (2010) |
| Druh dokumentu: | article |
| ISSN: | 1085-3375 1687-0409 |
| DOI: | 10.1155/2010/286040 |
| Popis: | Let a(t),b(t) be continuous T-periodic functions with ∫0Tb(t)dt=0. We establish one stability criterion for the linear damped oscillator x′′+b(t)x′+a(t)x=0. Moreover, based on the computation of the corresponding Birkhoff normal forms, we present a sufficient condition for the stability of the equilibrium of the nonlinear damped oscillator x′′+b(t)x′+a(t)x+c(t)x2n-1+e(t,x)=0, where n≥2,c(t) is a continuous T-periodic function, e(t,x) is continuous T-periodic in t and dominated by the power x2n in a neighborhood of x=0. |
| Databáze: | Directory of Open Access Journals |
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