Nonlinear Hybrid Continuous/Discrete-Time ...

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Beschreibung

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.

Über den Autor

1) Prof. Dr. Marat Akhmet is a member of the Department of Mathematics, Middle East Technical University, Turkey. He is a specialist in dynamical models, bifurcation theory, chaos theory and differential equations. He has spent several years investigating the dynamics of neural networks, economic models and mechanical systems. He has published 4 books on different topics of dynamical systems.
2) Dr. Ardak Kashkynbayev obtained his PhD from the Department of Mathematics, Middle East Technical University, Turkey. His research focuses on differential equations, bifurcation theory, chaos theory and applications to mechanical systems.

Zusammenfassung

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

Includes supplementary material: [...]

Inhaltsverzeichnis

1. Introduction.- 2. Linear and quasi-linear systems with piecewise constant argument.- 3. The reduction principle for systems with piecewise constant argument.- 4. The small parameter and differential equations with piecewise constant argument.- 5. Stability.- 6. The state-dependent piecewise constant argument.- 7. Almost periodic solutions.- 8. Stability of neural networks.- 9. The blood pressure distribution.- 10. Integrate-and-fire biological oscillators.

Details

Erscheinungsjahr:	2013
Fachbereich:	Analysis
Genre:	Importe , Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Reihe:	Atlantis Studies in Mathematics for Engineering and Science
Inhalt:	xiii 216 S. 4 s/w Illustr. 19 farbige Illustr.
ISBN-13:	9789491216381
ISBN-10:	9491216384
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Akhmet, Marat
Hersteller:	Atlantis Press Atlantis Studies in Mathematics for Engineering and Science
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 13 mm
Von/Mit:	Marat Akhmet
Erscheinungsdatum:	15.07.2013
Gewicht:	0,359 kg