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Nonlinear hybrid continuous/discrete-time models

Author: Marat Akhmet
Publisher: Amsterdam : Atlantis Press, ©2011.
Series: Atlantis studies in mathematics for engineering and science, v. 8.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
Summary:
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  Read more...
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Genre/Form: Electronic books
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Marat Akhmet
ISBN: 9789491216039 9491216031
OCLC Number: 733543756
Description: 1 online resource (xiii, 216 p.)
Contents: Linear and quasi-linear systems with piecewise constant argument --
The reduction principle for systems with piecewise constant argument --
The small parameter and differential equations with piecewise constant argument --
Stability --
The state-dependent piecewise constant argument --
Almost periodic solutions --
Stability of neural networks --
The blood pressure distribution --
Integrate-and-fire biological oscillators.
Series Title: Atlantis studies in mathematics for engineering and science, v. 8.
Responsibility: Marat Akhmet.

Abstract:

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.

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