Ordinary differential systems describing hysteresis effects and numerical simulations
type: Item
instance of: scholarly article
title: Ordinary differential systems describing hysteresis effects and numerical simulations
zbMATH Open document ID: 1022.34038
DOI: 10.1155/S108533750220603X
author: Takanobu Okazaki
author: Nobuyuki Kenmochi
author: Emil Minchev
published in: Abstract and Applied Analysis
publication date: 2003-01-13T00:00:00Z
full work available at URL: https://eudml.org/doc/50352
review text: The authors consider a class of ordinary differential systems which describe input-output relations of hysteresis type and include, for example, scalar stop and play operators. The systems with scalar-valued controls (inputs) and solutions (outputs) consist of a scalar ordinary differential equation and a scalar differential inclusion, generical both with nonlinear terms. The main theoretical result is an existence-uniqueness theorem for the initial value problem. Furthermore, the authors present examples of numerical simulations for particular choices of the coefficients in the linear part of the system and particular choices of nonlinearities and observe various types of the behavior of orbits on the input-output plane. This includes clockwise and anti-clockwise behavior and a number of long-term scenarios like convergence of orbits to an equilibrium, to a periodic orbit as well as to some point at infinity.
Mathematics Subject Classification ID: 34C55
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 1852861
zbMATH Keywords: hysteresis nonlinearity
zbMATH Keywords: initial value problem
zbMATH Keywords: orientation of hysteresis loop
zbMATH Keywords: long-term behavior of orbits
zbMATH Keywords: scalar differential inclusion
reviewed by: Dmitrii Rachinskii
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1852861