Random perturbations of parametric autoresonance

被引：1

作者：

Sultanov, Oskar ^{[1
,2
]}

机构：

[1] Russian Acad Sci, Ufa Sci Ctr, Inst Math, 112 Chernyshevsky St, Ufa 450008, Russia

[2] Peoples Friendship Univ Russia RUDN Univ, 6 Miklukho Maklaya St, Moscow 117198, Russia

来源：

NONLINEAR DYNAMICS | 2017年 / 89卷 / 04期

关键词：

Nonlinear system; Autoresonance; Random perturbation; Stability analysis; STABILITY; MODELS; SYSTEMS; PLASMAS;

D O I：

10.1007/s11071-017-3625-8

中图分类号：

TH [机械、仪表工业];

学科分类号：

0802 ;

摘要：

We consider a system of two nonlinear differential equations describing the capture into autoresonance in nonlinear oscillators under small parametric driving. Solutions with an infinitely growing amplitude are associated with the autoresonance phenomenon. Stability of such solutions is of great importance because only stable solutions correspond to physically observable motions. We study stability of autoresonant solutions with power asymptotics and show that the random fluctuations of the driving cannot destroy the capture into the parametric autoresonance.

引用

页码：2785 / 2793

页数：9

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