Investigation of the stability of an ODE-based hysteresis model

The aim of the paper is the comprehensive examination of a powerful hysteresis model, in which the hysteretic nonlinear behavior appears as a solution of an ordinary differential equation (ODE). One of the main advantages of the model is that the numerical solution of the ODE can be acquired easily and the model implementation into field problems can be handled by means of coupling the “hysteresis” equation to the equations of the problem. On the other hand since the model has the form of an ODE, there are many advanced tools for the investigation of the structure and the solutions of the equation. In the paper an analytical expression of a Poicnare-map is presented as the proof of stability.