Nonlinear Hybrid Continuous/Discrete-Time Models (Atlantis Studies in Mathematics for Engineering and Science, 8) - Hardcover

Akhmet, Marat

Hardcover

ISBN 10: 9491216023 ISBN 13: 9789491216022

Publisher: Atlantis Press, 2011

Synopsis

The book is mainly about hybrid systems with continuous/discrete-time dynamics. The major part of the book consists of the theory of equations with piece-wise constant argument of generalized type. The systems as well as technique of investigation were introduced by the author very recently. They both generalized known theory about differential equations with piece-wise constant argument, introduced by K. Cook and J. Wiener in the 1980s. Moreover, differential equations with fixed and variable moments of impulses are used to model real world problems. We consider models of neural networks, blood pressure distribution and a generalized model of the cardiac pacemaker. All the results of the manuscript have not been published in any book, yet. They are very recent and united with the presence of the continuous/discrete dynamics of time. It is of big interest for specialists in biology, medicine, engineering sciences, electronics. Theoretical aspects of the book meet very strong expectations of mathematicians who investigate differential equations with discontinuities of any type.

About this title

From the Back Cover

Most general differential equations with piece-wise constant argument are investigated

New technique of analysis is used. A new model of blood pressure distribution is introduced with complete analysis Synchronization of quite identical integrate-and-fire oscillators is proved

General model of quite identical integrate-and-fire oscillators is constructed

Model of recurrent neural networks with continuous/discrete-time is investigated

Review

From the reviews:

“Hybrid systems are a recent concept in dynamical systems theory and have important and extensive applications. ... The present book generalizes the concept of differential equations with piecewise constant argument by considering a more general type of equations and develops new methodological approaches to explore those challenging systems. ... This book is well written and readable and will be extremely useful not only to expert readers but also to graduate and advanced undergraduate students.” (Meng Fan, Mathematical Reviews, January, 2013)

Edition details

• Publisher: Atlantis Press
• Publication date: 2011
• Language: English
• ISBN 10: 9491216023
• ISBN 13: 9789491216022
• Binding: Hardcover
• Number of pages: 229