Nonlinear Hybrid Continuous/Discrete-Time Models
(Sprache: Englisch)
This book examines the author's recently-introduced theory of equations with piece-wise constant argument of generalized type, demonstrating its use in the modeling of such real world problems as neural networks, blood pressure distribution and others.
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This book examines the author's recently-introduced theory of equations with piece-wise constant argument of generalized type, demonstrating its use in the modeling of such real world problems as neural networks, blood pressure distribution and others.
Klappentext zu „Nonlinear Hybrid Continuous/Discrete-Time Models “
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.
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.
Inhaltsverzeichnis zu „Nonlinear Hybrid Continuous/Discrete-Time Models “
1. Introduction2. 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
Bibliographische Angaben
- Autor: Marat Akhmet
- 2011, 1st ed., XIII, 216 Seiten, Masse: 17,3 x 24,3 cm, Gebunden, Englisch
- Verlag: Springer, Berlin
- ISBN-10: 9491216023
- ISBN-13: 9789491216022
Sprache:
Englisch
Pressezitat
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)
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