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001435106 001__ 1435106
001435106 003__ OCoLC
001435106 005__ 20230309003836.0
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001435106 019__ $$a1244626872$$a1253402826
001435106 020__ $$a9783030645335$$q(electronic bk.)
001435106 020__ $$a3030645339$$q(electronic bk.)
001435106 020__ $$z9783030645342$$q(print)
001435106 020__ $$z3030645347
001435106 020__ $$z9783030645359$$q(print)
001435106 020__ $$z3030645355
001435106 020__ $$z9783030645328
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001435106 0247_ $$a10.1007/978-3-030-64533-5$$2doi
001435106 035__ $$aSP(OCoLC)1243514212
001435106 040__ $$aYDX$$beng$$erda$$epn$$cYDX$$dGW5XE$$dEBLCP$$dOCLCO$$dOCLCF$$dVT2$$dLIP$$dUKAHL$$dOCLCQ$$dOCLCO$$dCOM$$dSFB$$dWAU$$dOCLCQ
001435106 049__ $$aISEA
001435106 050_4 $$aQA380
001435106 08204 $$a515/.392$$223
001435106 1001_ $$aChurch, Kevin E. M.,$$eauthor.
001435106 24510 $$aBifurcation theory of impulsive dynamical systems /$$cKevin E.M. Church, Xinzhi Liu.
001435106 264_1 $$aCham, Switzerland :$$bSpringer,$$c[2021]
001435106 300__ $$a1 online resource (xvii, 388 pages) :$$billustrations (some color)
001435106 336__ $$atext$$btxt$$2rdacontent
001435106 337__ $$acomputer$$bc$$2rdamedia
001435106 338__ $$aonline resource$$bcr$$2rdacarrier
001435106 347__ $$atext file
001435106 347__ $$bPDF
001435106 4901_ $$aIFSR international series in systems science and systems engineering,$$x1574-0463 ;$$vvolume 34
001435106 504__ $$aIncludes bibliographical references and index.
001435106 5050_ $$aImpulsive functional differential equations. Introduction -- General linear systems -- Linear periodic systems -- Nonlinear systems and stability -- Existence, regularity and invariance of centre manifolds -- Computational aspects of centre manifolds -- Hyperbolicity and the classical hierarchy of invariant manifolds -- Smooth bifurcations -- Finite-dimensional ordinary impulsive differential equations. Preliminaries -- Linear systems -- Stability for nonlinear systems -- Invariant manifold theory -- Bifurcations -- Singluar and nonsmooth phenomena. Continuous approximation -- Non-smooth bifurcations -- Applications. Bifurcations in an impulsively damped or driven pendulum -- The Hutchinson equation with pulse harvesting -- Delayed SIR model with pulse vaccinaton and temporary immunity -- Stage-structured predator-prey system with pulsed birth -- Dynamics of an in-host viral infection model with drug treatment.
001435106 506__ $$aAccess limited to authorized users.
001435106 520__ $$aThis monograph presents the most recent progress in bifurcation theory of impulsive dynamical systems with time delays and other functional dependence. It covers not only smooth local bifurcations, but also some non-smooth bifurcation phenomena that are unique to impulsive dynamical systems. The monograph is split into four distinct parts, independently addressing both finite and infinite-dimensional dynamical systems before discussing their applications. The primary contributions are a rigorous nonautonomous dynamical systems framework and analysis of nonlinear systems, stability, and invariant manifold theory. Special attention is paid to the centre manifold and associated reduction principle, as these are essential to the local bifurcation theory. Specifying to periodic systems, the Floquet theory is extended to impulsive functional differential equations, and this permits an exploration of the impulsive analogues of saddle-node, transcritical, pitchfork and Hopf bifurcations. Readers will learn how techniques of classical bifurcation theory extend to impulsive functional differential equations and, as a special case, impulsive differential equations without delays. They will learn about stability for fixed points, periodic orbits and complete bounded trajectories, and how the linearization of the dynamical system allows for a suitable definition of hyperbolicity. They will see how to complete a centre manifold reduction and analyze a bifurcation at a nonhyperbolic steady state.
001435106 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed April 16, 2021).
001435106 650_0 $$aBifurcation theory.
001435106 650_0 $$aSystem analysis.
001435106 650_0 $$aDynamics.
001435106 650_0 $$aMathematical models.
001435106 650_6 $$aThéorie de la bifurcation.
001435106 650_6 $$aAnalyse de systèmes.
001435106 650_6 $$aDynamique.
001435106 650_6 $$aModèles mathématiques.
001435106 655_0 $$aElectronic books.
001435106 7001_ $$aLiu, Xinzhi,$$d1956-$$eauthor.
001435106 77608 $$iPrint version:$$z9783030645328$$w(OCoLC)1202060475
001435106 830_0 $$aIFSR international series on systems science and engineering ;$$vv. 34.$$x1574-0463
001435106 852__ $$bebk
001435106 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-030-64533-5$$zOnline Access$$91397441.1
001435106 909CO $$ooai:library.usi.edu:1435106$$pGLOBAL_SET
001435106 980__ $$aBIB
001435106 980__ $$aEBOOK
001435106 982__ $$aEbook
001435106 983__ $$aOnline
001435106 994__ $$a92$$bISE