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Bifurcation in Autonomous and Nonautonomous Differential Equations with Discontinuities

  • Marat Akhmet
  • Ardak Kashkynbayev

Part of the Nonlinear Physical Science book series (NPS)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Marat Akhmet, Ardak Kashkynbayev
    Pages 1-9
  3. Marat Akhmet, Ardak Kashkynbayev
    Pages 11-63
  4. Marat Akhmet, Ardak Kashkynbayev
    Pages 65-96
  5. Marat Akhmet, Ardak Kashkynbayev
    Pages 97-122
  6. Marat Akhmet, Ardak Kashkynbayev
    Pages 123-144
  7. Back Matter
    Pages 157-166

About this book

Introduction

This book is devoted to bifurcation theory for autonomous and nonautonomous differential equations with discontinuities of different types. That is, those with jumps present either in the right-hand-side or in trajectories or in the arguments of solutions of equations. The results obtained in this book can be applied to various fields such as neural networks, brain dynamics, mechanical systems, weather phenomena, population dynamics, etc. Without any doubt, bifurcation theory should be further developed to different types of differential equations. In this sense, the present book will be a leading one in this field. The reader will benefit from the recent results of the theory and will learn in the very concrete way how to apply this theory to differential equations with various types of discontinuity. Moreover, the reader will learn new ways to analyze nonautonomous bifurcation scenarios in these equations. The book will be of a big interest both for  beginners and experts in the field. For the former group of specialists, that is, undergraduate and graduate students, the book will be useful since it provides a strong impression that bifurcation theory can be developed not only for discrete and continuous systems, but those which combine these systems in very different ways. The latter group of specialists will find in this book several powerful instruments developed for the theory of discontinuous dynamical systems with variable moments of impacts, differential equations with piecewise constant arguments of generalized type and Filippov systems. A significant benefit of the present book is expected to be for those who consider bifurcations in systems with impulses since they are presumably nonautonomous systems.

Keywords

Hopf bifurcation Nonautonomous bifurcation Piecewise constant argument Discontinuous Right-Hand Side Impulsive Systems discontinuous dynamical systems Center manifold theory

Authors and affiliations

  • Marat Akhmet
    • 1
  • Ardak Kashkynbayev
    • 2
  1. 1.Department of MathematicsMiddle East Technical UniversityAnkaraTurkey
  2. 2.Department of MathematicsMiddle East Technical UniversityAnkaraTurkey

Bibliographic information

  • DOI https://doi.org/10.1007/978-981-10-3180-9
  • Copyright Information Springer Nature Singapore Pte Ltd. and Higher Education Press 2017
  • Publisher Name Springer, Singapore
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-981-10-3179-3
  • Online ISBN 978-981-10-3180-9
  • Series Print ISSN 1867-8440
  • Series Online ISSN 1867-8459
  • Buy this book on publisher's site