Dynamics of a second-order nonlinear equation with a large coefficient of delay control
The author studies the nonlinear second-order differential equation with delay control \[ \begin{aligned} \ddot U=F&(U,\dot U)+\lambda[\dot U(t-T)-\dot U] \\ +&\lambda\alpha[U(t-T)-U], \end{aligned} \] with a nonlinear function \(F,\) the delay coefficient \(T\) and the delay control coefficient \(\lambda,\) which is assumed to be positive and large, \(\alpha>0\) is a constant. Using the averaging principle and the principal asymptotic approximation techniques, an asymptotic expansion of the solutions for \(\epsilon=\lambda^{-1}\to 0^+\) is constructed.
scientific article; zbMATH DE number 6381293