Systems with Hysteresis

Hysteresis phenomena are common in numerous physical, mechanical, ecological and biological systems. They reflect memory effects and process irreversibility. The use of hysteresis operators (hysterons) offers an approach to macroscopic modelling of the dynamics of phase transitions and rheological systems. The applications cover processes in electromagnetism, elastoplasticity and population dynamics in particular. Hysterons are also typical elements of control systems where they represent thermostats and other discontinuous controllers with memory. The book offers the first systematic mathematical treatment of hysteresis nonlinearities. Construction procedures are set up for hysterons in various function spaces, in continuous and discontinuous cases. A general theory of variable hysterons is developed, including identification and stability questions. Both deterministic and non-deterministic hysterons are considered, with applications to the study of feedback systems. Many of the results presented - mostly obtained by the authors and their scientific group - have not been published before. The book is essentially self contained and is addressed both to researchers and advanced students. Front Matter....Pages I-XVIII Static hysteron....Pages 1-58 Identification theorem....Pages 59-93 Vibro-correct differential equations and variable hysterons....Pages 94-150 Multidimensional hysterons....Pages 151-211 Discontinuous nonlinearities....Pages 212-273 Self-Magnetization Phenomenon....Pages 274-319 Complex hysteresis nonlinearities....Pages 320-396 Back Matter....Pages 397-410 Static Hysteron Identification Theorem Vibro-Correct Differential Equations and Variable Hysterons Multidimensional Hysterons Discontinuous Nonlinearities Self-Magnetization Phenomenon Complex Hysteresis Nonlinearities Bibliographic Comments References Subject Index.