Nonlinear dynamics of piecewise constant systems and implementation of piecewise constant arguments.

*(English)*Zbl 1154.70001
Hackensack, NJ: World Scientific (ISBN 978-981-281-850-8/hbk; 978-981-281-851-5/ebook). xvi, 328 p. (2008).

This book provides the methodology for analyzing and assessing nonlinear piecewise constant systems on a theoretically and practically sound basis. Piecewise constant systems exist in widely expanded areas such as biomedicine, chemistry, mechanical engineering, physics, civil engineering, aerodynamical engineering, etc.

The material of the book consists of four components: concept and solution developments, characteristics, numerical approaches and applications of piecewise constant theories to dynamic systems. The chapters of the book are arranged in such a way that each topic is self-contained, and the main concepts are explained fully with necessary details. The reader may gain the main concepts of each chapter with as less as possible the need to refer to the other chapters; therefore, the reader may start to read one or more chapters of the book for its own interests.

The author uses the theory of piecewise constant functions for nonlinear dynamic analysis and for establishing a novel criterion (named periodicity-ratio criterion) to derive irregular and chaotic solutions from regular solutions of nonlinear dynamic systems. The newly established numerical method provides efficient numerical calculations with good convergence and high accuracy. These research results make the book valuable to specialists in nonlinear mechanics.

The material of the book consists of four components: concept and solution developments, characteristics, numerical approaches and applications of piecewise constant theories to dynamic systems. The chapters of the book are arranged in such a way that each topic is self-contained, and the main concepts are explained fully with necessary details. The reader may gain the main concepts of each chapter with as less as possible the need to refer to the other chapters; therefore, the reader may start to read one or more chapters of the book for its own interests.

The author uses the theory of piecewise constant functions for nonlinear dynamic analysis and for establishing a novel criterion (named periodicity-ratio criterion) to derive irregular and chaotic solutions from regular solutions of nonlinear dynamic systems. The newly established numerical method provides efficient numerical calculations with good convergence and high accuracy. These research results make the book valuable to specialists in nonlinear mechanics.

Reviewer: Vasile Marinca (Timişoara)