Bifurcation in Autonomous and Nonautonomous Differential Equations with Discontinuities

1. Auflage 2017
ISBN: 978-981-10-3179-3
Verlag: Springer

Buch, Englisch, 166 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 3967 g

Reihe: Nonlinear Physical Science

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.

Zielgruppe

Research

Autoren/Hrsg.

Akhmet, Marat

Kashkynbayev, Ardak

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Nichtlineare Wissenschaft
• Mathematik | Informatik Mathematik Geometrie Dynamische Systeme
• Technische Wissenschaften Elektronik | Nachrichtentechnik Nachrichten- und Kommunikationstechnik Regelungstechnik

Inhaltsverzeichnis

Introduction.- Hopf Bifurcation in Impulsive Systems.- Hopf Bifurcation in Fillopov Systems.- Nonautonomous Transcritical and Pitchfork Bifurcations in an Impulsive Bernoulli Equations.- Nonautonomous Transcritical and Pitchfork Bifurcations in Scalar Non-solvable Impulsive Differential Equations.- Nonautonomous Transcritical and Pitchfork Bifurcations in Bernoulli Equations with Piecewise Constant Argument of Generalized Type.

Über Autor(innen)

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.