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

溺愛

Nonlinear Systems and StabilityThis chapter contains a proof of the principle of linearized stability for nonlinear impulsive functional differential equations, in addition to some auxiliary results on smooth dependence on initial conditions.

品嘗你的人

模范

Computational Aspects of Centre ManifoldsA follow-up to Chapter ., this chapter is devoted to computational aspects of centre manifold theory. This includes a concrete representation of the centre manifold in Euclidean space, Taylor expansions, and an explicit ordinary impulsive differential equation for the dynamics on the manifold.

floodgate

Hyperbolicity and the Classical Hierarchy of Invariant ManifoldsWe discuss the existence and smoothness of unstable, stable and centre-stable manifolds, thereby establishing the classical hierarchy of invariant manifolds for impulsive functional differential equations.

LIMN

夾死提手勢

Myocyte

MAIZE

BifurcationsThis chapter presents analogues of the classical codimension-one bifurcations of flows and maps. Specifically, this includes analogues of the fold (saddle-node), period-doubling, and Hopf (Neimark-Sacker) bifurcation. Additionally, we present the transcritical and pitchfork bifurcations.

badinage

淘氣

Introductionocesses, these bursts of activity are sometimes intrinsic to the dynamics. For example, the Hodgkin–Huxley model [.] is a nonlinear ordinary differential equation that describes the propagation of action potentials of neurons; here, the bursts of activity correspond to the action potentials and are