Asymptotic behavior and its visualization of the solutions of intermittently and impulsively damped nonlinear oscillator equations

摘要

Intermittently damped oscillators are of importance both in practice and in attractivity investigation. The “on-off” dampings with very short “on” intervals are transient cases between non-asymptotic stability and asymptotic stability. In this paper, we concentrate the “on” intervals into single points. We also investigate the asymptotic behavior of the impulsive equation ẍ+f(ξ)=0 (t≠tn; ξ̇(tn+0)=bnξ̇(tn) (t=tn) (n = 1,2…). We find an analogy to the attractivity results for distributed damping. The problems and the solutions appear more clearly in the case of impulsive damping. We illustrate the theoretical results with figures made by program packages developed in Mathematica.