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Bifurcation theory of impulsive dyna...

Church, Kevin E. M.

Bifurcation theory of impulsive dynamical systems

Record Type:	Electronic resources : Monograph/item
Title/Author:	Bifurcation theory of impulsive dynamical systemsby Kevin E. M. Church, Xinzhi Liu.
Author:	Church, Kevin E. M.
other author:	Liu, Xinzhi.
Published:	Cham :Springer International Publishing :2021.
Description:	xvii, 388 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Bifurcation theory.
Online resource:	https://doi.org/10.1007/978-3-030-64533-5
ISBN:	9783030645335$q(electronic bk.)

Bifurcation theory of impulsive dynamical systems
Church, Kevin E. M.

Bifurcation theory of impulsive dynamical systems[electronic resource] /by Kevin E. M. Church, Xinzhi Liu. - Cham :Springer International Publishing :2021. - xvii, 388 p. :ill. (some col.), digital ;24 cm. - IFSR international series in systems science and systems engineering,v.341574-0463 ;. - IFSR international series in systems science and systems engineering ;23..

Impulsive functional differential equations -- Preliminaries -- General linear systems -- Linear periodic systems -- Nonlinear systems and stability -- Invariant manifold theory -- Smooth bifurcations -- Finite-dimensional ordinary impulsive differential equations -- Preliminaries -- Linear systems -- Stability for nonlinear systems -- Invariant manifold theory -- Bifurcations -- Special topics and applications -- Continuous approximation -- Non-smooth bifurcations -- Bifurcations in models from mathematical epidemiology and ecology.

This monograph presents the most recent progress in bifurcation theory of impulsive dynamical systems with time delays and other functional dependence. It covers not only smooth local bifurcations, but also some non-smooth bifurcation phenomena that are unique to impulsive dynamical systems. The monograph is split into four distinct parts, independently addressing both finite and infinite-dimensional dynamical systems before discussing their applications. The primary contributions are a rigorous nonautonomous dynamical systems framework and analysis of nonlinear systems, stability, and invariant manifold theory. Special attention is paid to the centre manifold and associated reduction principle, as these are essential to the local bifurcation theory. Specifying to periodic systems, the Floquet theory is extended to impulsive functional differential equations, and this permits an exploration of the impulsive analogues of saddle-node, transcritical, pitchfork and Hopf bifurcations. Readers will learn how techniques of classical bifurcation theory extend to impulsive functional differential equations and, as a special case, impulsive differential equations without delays. They will learn about stability for fixed points, periodic orbits and complete bounded trajectories, and how the linearization of the dynamical system allows for a suitable definition of hyperbolicity. They will see how to complete a centre manifold reduction and analyze a bifurcation at a nonhyperbolic steady state.

ISBN: 9783030645335$q(electronic bk.)

Standard No.: 10.1007/978-3-030-64533-5doiSubjects--Topical Terms:

185804
Bifurcation theory.

LC Class. No.: QA380

Dewey Class. No.: 515.392

Bifurcation theory of impulsive dynamical systems
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245 1 0 $a Bifurcation theory of impulsive dynamical systems $h [electronic resource] / $c by Kevin E. M. Church, Xinzhi Liu.
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300 $a xvii, 388 p. : $b ill. (some col.), digital ; $c 24 cm.
490 1 $a IFSR international series in systems science and systems engineering, $x 1574-0463 ; $v v.34
505 0 $a Impulsive functional differential equations -- Preliminaries -- General linear systems -- Linear periodic systems -- Nonlinear systems and stability -- Invariant manifold theory -- Smooth bifurcations -- Finite-dimensional ordinary impulsive differential equations -- Preliminaries -- Linear systems -- Stability for nonlinear systems -- Invariant manifold theory -- Bifurcations -- Special topics and applications -- Continuous approximation -- Non-smooth bifurcations -- Bifurcations in models from mathematical epidemiology and ecology.
520 $a This monograph presents the most recent progress in bifurcation theory of impulsive dynamical systems with time delays and other functional dependence. It covers not only smooth local bifurcations, but also some non-smooth bifurcation phenomena that are unique to impulsive dynamical systems. The monograph is split into four distinct parts, independently addressing both finite and infinite-dimensional dynamical systems before discussing their applications. The primary contributions are a rigorous nonautonomous dynamical systems framework and analysis of nonlinear systems, stability, and invariant manifold theory. Special attention is paid to the centre manifold and associated reduction principle, as these are essential to the local bifurcation theory. Specifying to periodic systems, the Floquet theory is extended to impulsive functional differential equations, and this permits an exploration of the impulsive analogues of saddle-node, transcritical, pitchfork and Hopf bifurcations. Readers will learn how techniques of classical bifurcation theory extend to impulsive functional differential equations and, as a special case, impulsive differential equations without delays. They will learn about stability for fixed points, periodic orbits and complete bounded trajectories, and how the linearization of the dynamical system allows for a suitable definition of hyperbolicity. They will see how to complete a centre manifold reduction and analyze a bifurcation at a nonhyperbolic steady state.
650 0 $a Bifurcation theory. $3 185804
650 0 $a System analysis. $3 182013
650 0 $a Dynamics. $3 189568
650 0 $a Mathematical models. $3 182479
650 1 4 $a Dynamical Systems and Ergodic Theory. $3 273794
650 2 4 $a Vibration, Dynamical Systems, Control. $3 274667
650 2 4 $a Analysis. $3 273775
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950 $a Mathematics and Statistics (SpringerNature-11649)