ASYMPTOTIC-BEHAVIOR AND ITS VISUALIZATION OF THE SOLUTIONS OF INTERMITTENTLY AND IMPULSIVELY DAMPED NONLINEAR OSCILLATOR EQUATIONS

Authors
Citation
J. Karsai, ASYMPTOTIC-BEHAVIOR AND ITS VISUALIZATION OF THE SOLUTIONS OF INTERMITTENTLY AND IMPULSIVELY DAMPED NONLINEAR OSCILLATOR EQUATIONS, Applied mathematics and computation, 89(1-3), 1998, pp. 161-172
Citations number
8
Categorie Soggetti
Mathematics,Mathematics
ISSN journal
00963003
Volume
89
Issue
1-3
Year of publication
1998
Pages
161 - 172
Database
ISI
SICI code
0096-3003(1998)89:1-3<161:AAIVOT>2.0.ZU;2-J
Abstract
Intermittently damped oscillators are of importance both in practice a nd in attractivity investigation. The ''on-off'' dampings with very sh ort ''on'' intervals are transient cases between non-asymptotic stabil ity and asymptotic stability. In this paper, we concentrate the ''on'' intervals into single points. We also investigate the asymptotic beha vior of the impulsive equation <(x)double over dot>+f(x)=0 (t not equa l t(n)); <(x)over dot>(t(n)+0)=b(n)<(x)over dot>(t(n)) (t=t(n)) (n = 1 ,2...). We find an analogy to the attractivity results for distributed damping. The problems and the solutions appear more clearly in the ca se of impulsive damping. We illustrate the theoretical results with fi gures made by program packages developed in Mathematica. (C) Elsevier Science Inc., 1998.