On the analysis of quasi-periodic systems and a novel “deterministic” explanation of the stochastic resonance phenomenon

Abstract

The present paper is concerned with the analysis of quasi-periodic systems which represent an important class of dynamical systems frequently encountered in applications. The related problems appear, e.g. in the analysis of parametric amplifiers based on resonant micro- and nanoscale systems, wave propagation in nearly periodic structures and composite materials, etc. The conventional methods of linear and nonlinear dynamics, e.g. asymptotic methods and approximate approaches based on Floquet theory, often appear to be not applicable for solving such problems. The present paper addresses the application of the Oscillatory Strobodynamics approach and the Method of Varying Amplitudes for these problems with the notable effects being revealed. In particular, a novel “deterministic” explanation to the phenomenon of stochastic resonance is proposed.