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Bifurcation in Autonomous and Nonautonomous Differential Equations with Discontinuities

  • Book
  • © 2017

Overview

Authors:
  1. Marat Akhmet

    1. Department of Mathematics, Middle East Technical University, Ankara, Turkey

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    You can also search for this author in PubMed   Google Scholar

  2. Ardak Kashkynbayev

    1. Department of Mathematics, Middle East Technical University, Ankara, Turkey

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Offers illustrations for nonautonomous bifurcation, for the first time
  • Applies bifurcation theory to differential and hybrid systems
  • Discusses the latest mathematical problems that are confirmed in the most recently introduced types of differential equations
  • Shows how to apply bifurcation theory to differential equations with various types of discontinuity in a very concrete way
  • Includes supplementary material: sn.pub/extras

Part of the book series: Nonlinear Physical Science (NPS)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xi
    Download chapter PDF

  2. Introduction

    • Marat Akhmet, Ardak Kashkynbayev
    Pages 1-9

  3. Hopf Bifurcation in Impulsive Systems

    • Marat Akhmet, Ardak Kashkynbayev
    Pages 11-63

  4. Hopf Bifurcation in Filippov Systems

    • Marat Akhmet, Ardak Kashkynbayev
    Pages 65-96

  5. Nonautonomous Bifurcation in Impulsive Bernoulli Equations

    • Marat Akhmet, Ardak Kashkynbayev
    Pages 97-122

  6. Nonautonomous Bifurcations in Nonsolvable Impulsive Systems

    • Marat Akhmet, Ardak Kashkynbayev
    Pages 123-144

  7. Nonautonomous Bifurcations in Bernoulli Differential Equations with Piecewise Constant Argument of Generalized Type

    • Marat Akhmet, Ardak Kashkynbayev
    Pages 145-156

  8. Back Matter

    Pages 157-166
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Keywords

About this book

This book focuses on bifurcation theory for autonomous and nonautonomous differential equations with discontinuities of different types – those with jumps present either in the right-hand side, or in trajectories or in the arguments of solutions of equations. The results obtained can be applied to various fields, such as neural networks, brain dynamics, mechanical systems, weather phenomena and population dynamics. Developing bifurcation theory for various types of differential equations, the book is pioneering in the field. It presents the latest results and provides a practical guide to applying the theory to differential equations with various types of discontinuity. Moreover, it offers new ways to analyze nonautonomous bifurcation scenarios in these equations. As such, it shows undergraduate and graduate students how bifurcation theory can be developed not only for discrete and continuous systems, but also for those that combine these systems in very different ways. At the same time, it offers specialists several powerful instruments developed for the theory of discontinuous dynamical systems with variable moments of impact, differential equations with piecewise constant arguments of generalized type and Filippov systems.


Reviews

“The book under review deals with bifurcation theory for discontinuous dynamical systems. … This book is also appropriate for a graduate course on the subject of discontinuous differential equations. A vast list of references is presented.” (Ronaldo Alves Garcia, Mathematical Reviews, January, 2018)

Authors and Affiliations

  • Department of Mathematics, Middle East Technical University, Ankara, Turkey

    Marat Akhmet, Ardak Kashkynbayev

About the authors

1) Prof. Dr. Marat Akhmet is a member of the Department of Mathematics, Middle East Technical University, Turkey. He is a specialist in dynamical  models, bifurcation theory, chaos theory and differential equations. He has spent several years investigating the dynamics of neural networks, economic models and mechanical systems. He has published 4 books on different topics of dynamical systems.

2)  Dr. Ardak Kashkynbayev obtained his PhD from the Department of Mathematics, Middle East Technical University, Turkey. His research focuses on differential equations, bifurcation theory, chaos theory and applications to mechanical systems.

 

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