On the eigenvalue spectrum for time-delayed Floquet problems
The author investigates linear homogeneous scalar differential-difference equations with harmonic time dependence of the type \[ dx(t)/dt = cx(t) + B(t)x(t - r) \] where the coefficient \(B(t)\) is periodic in time: \(B (t) = B (t + T)\) and \(c\) is a constant. The associated eigenvalue problem is solved in terms of a continued fraction expansion for the characteristic equation. In addition, the dependence of the largest eigenvalue on the system parameters is discussed in detail. The result suggests features to improve control of chaos by feedback schemes with time-dependent control amplitudes.
scientific article; zbMATH DE number 1474685