Abstract and Applied Analysis
Volume 7 (2002), Issue 11, Pages 563-583
doi:10.1155/S108533750220603X
Ordinary differential systems describing hysteresis effects and numerical simulations
Emil Minchev1
, Takanobu Okazaki1
and Nobuyuki Kenmochi3
1Department of Mathematics, Graduate School of Science and Technology, Chiba University, 1-33 Yayoi-chō, Inage-ku, Chiba 263-8522, Japan
3Department of Mathematics, Faculty of Education, Chiba University, 1-33 Yayoi-chō, Inage-ku, Chiba 263-8522, Japan
Abstract
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.