Название: Systems with Non-Smooth Inputs: Mathematical Models of Hysteresis Phenomena, Biological Systems, and Electric Circuits
Автор: Jurgen Appell, Nguyen Thi Hien, Lyubov Petrova, Irina Pryadko
Издательство: De Gruyter
Год: 2021
Страниц: 288
Язык: английский
Формат: pdf (true), epub
Размер: 31.1 MB

The authors present a completely new and highly application-oriented field of nonlinear analysis. The work covers the theory of non-smooth input-output systems and presents various methods to non-standard applications in mathematics and physics. A particular focus lies on hysteresis and relay phenomena, electric circuits with diode nonlinearities, and biological systems with constraints.

This book consists of two parts which may be summarized under the title Systems with non-smooth inputs. The first part (Chapters 1 and 2) is concerned with so-called systems with diode nonlinearities (or DN-systems, for short). This terminology was created by a group of teachers and collaborators of the Voronezh State University during the 1980th years working on the mathematical modelling and numerical investigation of electric circuits. To explain the theory, methods, and applications of this topic, let us briefly recall the structure of a simple electrical network.

The chapter 1 is concerned with so-called systems with diode nonlinearities (or DN-systems, for short). We discuss such systems first heuristically, and then provide the necessary mathematical tools like convex sets and cones. Afterwards we study electrical circuits with diode converters and prove existence and uniqueness theorems for solutions of Cauchy problems involving DN-systems, as well as existence and stability theorems for forced periodic oscillations, with a particular emphasis on planar systems. Finally, in an Appendix we present the Mathematica Programme which were helpful for drawing some of the numerous pictures.