Bifurcation theory of impulsive dynamical systems [electronic resource]

• 作者： Church, Kevin E. M.
• 其他作者：
  • Liu, Xinzhi.
  • SpringerLink (Online service)
• 其他題名：
  • IFSR international series in systems science and systems engineering ;
• 出版： Cham : Springer International Publishing :Imprint: Springer
• 叢書名： IFSR international series in systems science and systems engineering,v.34
• 主題： Bifurcation theory. , System analysis. , Dynamics. , Mathematical models. , Dynamical Systems and Ergodic Theory. , Vibration, Dynamical Systems, Control. , Analysis.
• ISBN： 9783030645335 (electronic bk.) 、 9783030645328 (paper)
• FIND@SFXID: CGU
• 資料類型: 電子書
• 內容註: 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.
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• 摘要註: 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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