TY - JOUR

T1 - Bifurcations of autoresonant modes in oscillating systems with combined excitation

AU - Sultanov, Oskar A.

PY - 2020/2/1

Y1 - 2020/2/1

N2 - A mathematical model describing the capture of nonlinear systems into the autoresonance by a combined parametric and external periodic slowly varying perturbation is considered. The autoresonance phenomenon is associated with solutions having an unboundedly growing amplitude and a limited phase mismatch. The paper investigates the behavior of such solutions when the parameters of the excitation take bifurcation values. In particular, the stability of different autoresonant modes is analyzed and the asymptotic approximations of autoresonant solutions on asymptotically long time intervals are proposed by a modified averaging method with using the constructed Lyapunov functions.

AB - A mathematical model describing the capture of nonlinear systems into the autoresonance by a combined parametric and external periodic slowly varying perturbation is considered. The autoresonance phenomenon is associated with solutions having an unboundedly growing amplitude and a limited phase mismatch. The paper investigates the behavior of such solutions when the parameters of the excitation take bifurcation values. In particular, the stability of different autoresonant modes is analyzed and the asymptotic approximations of autoresonant solutions on asymptotically long time intervals are proposed by a modified averaging method with using the constructed Lyapunov functions.

KW - asymptotics

KW - autoresonance

KW - bifurcation

KW - nonlinear equations

KW - stability

UR - http://www.scopus.com/inward/record.url?scp=85076432489&partnerID=8YFLogxK

U2 - 10.1111/sapm.12294

DO - 10.1111/sapm.12294

M3 - Article

AN - SCOPUS:85076432489

VL - 144

SP - 213

EP - 241

JO - Studies in Applied Mathematics

JF - Studies in Applied Mathematics

SN - 0022-2526

IS - 2

ER -