國立虎尾科技大學 |

Bifurcation in autonomous and nonautonomous differential equations with discontinuities

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Bifurcation in autonomous and nonautonomous differential equations with discontinuities/ by Marat Akhmet, Ardak Kashkynbayev.
Author:	Akhmet, Marat.
other author:	Kashkynbayev, Ardak.
Published:	Singapore :Springer Singapore : : 2017.,
Description:	xi, 166 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
Subject:	Bifurcation theory. -
Online resource:	http://dx.doi.org/10.1007/978-981-10-3180-9
ISBN:	9789811031809

Bifurcation in autonomous and nonautonomous differential equations with discontinuities
Akhmet, Marat.

Bifurcation in autonomous and nonautonomous differential equations with discontinuities[electronic resource] /by Marat Akhmet, Ardak Kashkynbayev. - Singapore :Springer Singapore :2017. - xi, 166 p. :ill., digital ;24 cm. - Nonlinear physical science,1867-8440. - Nonlinear physical science..

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.

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.

ISBN: 9789811031809

Standard No.: 10.1007/978-981-10-3180-9doiSubjects--Topical Terms:

527837
Bifurcation theory.

LC Class. No.: QA380

Dewey Class. No.: 515.392

Bifurcation in autonomous and nonautonomous differential equations with discontinuities
LDR:03216nam a2200325 a 4500 001 958546
003 DE-He213
005 20170817093916.0
006 m d
007 cr nn 008maaau
008 201118s2017 si s 0 eng d
020 $a 9789811031809 $q (electronic bk.)
020 $a 9789811031793 $q (paper)
024 7 $a 10.1007/978-981-10-3180-9 $2 doi
035 $a 978-981-10-3180-9
040 $a GP $c GP
041 0 $a eng
050 4 $a QA380
072 7 $a PBWR $2 bicssc
072 7 $a MAT034000 $2 bisacsh
082 0 4 $a 515.392 $2 23
090 $a QA380 $b .A315 2017
100 1 $a Akhmet, Marat. $3 788072
245 1 0 $a Bifurcation in autonomous and nonautonomous differential equations with discontinuities $h [electronic resource] / $c by Marat Akhmet, Ardak Kashkynbayev.
260 $a Singapore : $c 2017. $b Springer Singapore : $b Imprint: Springer,
300 $a xi, 166 p. : $b ill., digital ; $c 24 cm.
490 1 $a Nonlinear physical science, $x 1867-8440
505 0 $a 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.
520 $a 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.
650 0 $a Bifurcation theory. $3 527837
650 1 4 $a Mathematics. $3 527692
650 2 4 $a Dynamical Systems and Ergodic Theory. $3 671353
650 2 4 $a Control. $3 782232
650 2 4 $a Applications of Nonlinear Dynamics and Chaos Theory. $3 1113607
650 2 4 $a Difference and Functional Equations. $3 672077
650 2 4 $a Ordinary Differential Equations. $3 670854
700 1 $a Kashkynbayev, Ardak. $3 1250758
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer eBooks
830 0 $a Nonlinear physical science. $3 1067560
856 4 0 $u http://dx.doi.org/10.1007/978-981-10-3180-9
950 $a Physics and Astronomy (Springer-11651)