Titlebook: Bifurcation Theory of Impulsive Dynamical Systems; Kevin E.M. Church,Xinzhi Liu Book 2021 The Editor(s) (if applicable) and The Author(s),

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Smooth Bifurcationsl explain how the centre manifold reduction can be adapted to take into account parameters, prove two generic bifurcation patterns and present a general recipe for how one might study smooth local bifurcations in impulsive functional differential equations.

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Continuous Approximationin time but occurs on a negligibly small time scale. The intuition is that one can ignore the transient small-time intermediate dynamics and consider only the change in state. In this chapter, we explore the consequences of ignoring such small-time dynamics by continuously approximating the impulse

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Book 2021tion 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 l

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