Unbounded solutions for systems with hysteretic nonlinearity

Abstract

The work is dedicated to study of the dynamics of model systems that are described by differential equations with additive hysteretic nonlinearities in the case when a hysteretic loop bypass clockwise. In particular, for the model of the harmonic oscillator with hysteretic external force the conditions for existence of unbounded solutions are obtained. For the model of harmonic oscillator with a dry (Coulomb) and viscous friction under external hysteretic affection we obtained a set of conditions that ensure the self-oscillation mode. The numerical examples that illustrate the results of this work are also presented.