Nonlinear Hybrid Continuous/Discrete-Time Models

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.
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: sn.pub/extras

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Marat Akhmet

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blood pressure distribution hybrid systems with continuous/discrete-time integrate-and-fire biological oscillators neural networks piecewise constant argument ordinary differential equations

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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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