© 2011

Nonlinear Hybrid Continuous/Discrete-Time Models


Part of the Atlantis Studies in Mathematics for Engineering and Science book series (ASMES, volume 8)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Marat Akhmet
    Pages 1-15
  3. Marat Akhmet
    Pages 71-88
  4. Marat Akhmet
    Pages 105-119
  5. Marat Akhmet
    Pages 121-132
  6. Marat Akhmet
    Pages 133-174
  7. Marat Akhmet
    Pages 175-199
  8. Back Matter
    Pages 203-216

About this book


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.


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

Authors and affiliations

  1. 1.Dept. MathematicsMiddle East Technical University (METU)AnkaraTurkey

Bibliographic information


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)