Nonlinear Hybrid Continuous/Discrete-Time Models
1st Edition
Published on 3. May 2011
XIII, 216 pages
978-94-91216-03-9 (ISBN)
Description
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.
Reviews / Votes
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)
More details
Other editions
Additional editions
Marat Akhmet
Nonlinear Hybrid Continuous/Discrete-Time Models
Book
07/2013
Atlantis Press (Zeger Karssen)
€53.49
Shipment within 10-15 days
Marat Akhmet
Nonlinear Hybrid Continuous/Discrete-Time Models
Book
05/2011
Atlantis Press (Zeger Karssen)
€53.49
Shipment within 10-15 days
Content
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.
