Hysteretic nonlinearity and unbounded solutions in oscillating systems

Abstract

The paper is focused on the study of dynamics of oscillating systems described by differential equations with added hysteretic nonlinearities in the case when a hysteretic loop bypass clockwise. For the model of a harmonic oscillator with hysteretic external force, the conditions for existence of unbounded solutions are inferred from a theorem. For the model of a harmonic oscillator with viscous and Coulomb frictions, under external hysteretic perturbations, a set of conditions for the self-oscillation mode are obtained.