Periodic Convergence for a Class of Nonlinear Time-Delay Systems

The new existence conditions for periodic steady-state solution in time-delay convergent systems are presented. The main advantage of this result is that highly nonlinear (without meaningful linear approximation) dynamics are allowed for analysis. These conditions are developed for Persidskii and Lotka-Volterra time-delay systems. The efficiency of the approach is demonstrated on academic examples of these models.