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Field name	Details
Dewey Class	515.352
Title	Nonlinear Hybrid Continuous/Discrete-Time Models ([Ebook]) / by Marat Akhmet.
Author	Akhmet, Marat
Other name(s)	SpringerLink (Online service)
Publication	Paris : Atlantis Press , 2011.
Physical Details	XIV, 218 pages : online resource.
Series	Atlantis Studies in Mathematics for Engineering and Science 1875-7642 ; ; 8
ISBN	9789491216039
Summary Note	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.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	http://dx.doi.org/10.2991/978-94-91216-03-9
Links to Related Works	Subject References: Applications of Mathematics . Differential equation . Mathematics . Medicine . Medicine/Public Health, general . Ordinary differential equations . Physiological, Cellular and Medical Topics . Physiology . Authors: Akhmet, Marat . Corporate Authors: SpringerLink (Online service) . Series: Atlantis Studies in Mathematics for Engineering and Science . Classification: 515.352 . 515.352 (DDC 23) .

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Nonlinear Hybrid Continuous/Discrete-Time Models

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