Nonlinear Dynamical Systems with High-Speed Feedback

The aim of the work is to contribute to the qualitative and quantitative analysis of nonlinear dynamical systems of the second order with high-speed feedback, which can also be generally introduced into higher order systems which at present are gaining an increasing amount of popularity in use of the high-frequency oscillators in electronic circuits. Singular Perturbation Theory is the mathematical framework that yields the tools to explore the complicated dynamical behavior of these systems. The work gives an overview of some methods used to investigate the dynamics of singularly perturbed nonlinear systems, for which does not exist a comprehensive theory that would give us an overall view of their behavior. This issue is currently happening world wide, not only in the mathematical community when dealing with the theory and application of nonlinear dynamical systems, but also in the field of electrical engineering and automation.