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
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.