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Bifurcation Theory of Impulsive Dynamical Systems

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Bifurcation Theory of Impulsive Dynamical Systems/ by Kevin E.M. Church, Xinzhi Liu.
作者:	Church, Kevin E.M.
其他作者:	Liu, Xinzhi.
面頁冊數:	XVII, 388 p. 29 illus., 12 illus. in color.online resource. :
Contained By:	Springer Nature eBook
標題:	Dynamics. -
電子資源:	https://doi.org/10.1007/978-3-030-64533-5
ISBN:	9783030645335

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. - 1st ed. 2021. - XVII, 388 p. 29 illus., 12 illus. in color.online resource. - IFSR International Series in Systems Science and Systems Engineering,342698-5497 ;. - IFSR International Series in Systems Science and Systems Engineering,32.

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

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

592238
Dynamics.

LC Class. No.: QA313

Dewey Class. No.: 515.39

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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.
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