Abstract and Applied Analysis
Volume 7 (2002), Issue 11, Pages 563-583

Ordinary differential systems describing hysteresis effects and numerical simulations

Emil Minchev,1 Takanobu Okazaki,1 and Nobuyuki Kenmochi2

1Department of Mathematics, Graduate School of Science and Technology, Chiba University, 1-33 Yayoi-chō, Inage-ku, Chiba 263-8522, Japan
2Department of Mathematics, Faculty of Education, Chiba University, 1-33 Yayoi-chō, Inage-ku, Chiba 263-8522, Japan

Received 1 May 2002

Copyright © 2002 Emil Minchev et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We consider a general class of ordinary differential systems which describes input-output relations of hysteresis types, for instance, play or stop operators. The system consists of two first-order nonlinear ODEs and one of them includes a subdifferential operator depending on the unknowns. Our main objective of this paper is to give an existence-uniqueness result for the system as well as to give various numerical simulations of input-output relations which the system describes as typical cases.