TY - JOUR

T1 - Capture into parametric autoresonance in the presence of noise

AU - Sultanov, Oskar

PY - 2019/8/1

Y1 - 2019/8/1

N2 - System of differential equations describing the initial stage of the capture of nonlinear oscillations into the parametric autoresonance is considered. Of special interest are resonant solutions whose amplitude increases without bound with time. The stability of such solutions ensures the physical observability of the autoresonant capture. We study the stability of such solutions with respect to persistent perturbations of white noise type, and we show that under certain restrictions on the intensity of the noise, the capture into parametric autoresonance is preserved with probability tending to one.

AB - System of differential equations describing the initial stage of the capture of nonlinear oscillations into the parametric autoresonance is considered. Of special interest are resonant solutions whose amplitude increases without bound with time. The stability of such solutions ensures the physical observability of the autoresonant capture. We study the stability of such solutions with respect to persistent perturbations of white noise type, and we show that under certain restrictions on the intensity of the noise, the capture into parametric autoresonance is preserved with probability tending to one.

KW - Autoresonance

KW - Lyapunov function

KW - Stability

KW - Stochastic perturbation

UR - http://www.scopus.com/inward/record.url?scp=85063320400&partnerID=8YFLogxK

U2 - 10.1016/j.cnsns.2019.03.022

DO - 10.1016/j.cnsns.2019.03.022

M3 - Article

AN - SCOPUS:85063320400

VL - 75

SP - 14

EP - 21

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

SN - 1007-5704

ER -