New Methods for Proving the Existence and Stability of Periodic Solutions in Singularly Perturbed Delay Systems

We carry out a detailed analysis of the existence, asymptotics, and stability problems for periodic solutions that bifurcate from the zero equilibrium state in systems with large delay. The account is based on a specific meaningful example given by a certain scalar nonlinear second-order differential–difference equation that is a mathematical model of a single-circuit $RCL$-oscillator with delay in a feedback loop.