Abstract
A follow-up to Chapter 5, 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.
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Notes
- 1.
Note that \(Q_t^-(\theta ^+)=Q_t(\theta )\) for θ < 0.
References
M. Ait Babram, M.L. Hbid, O. Arino, Approximation scheme of a center manifold for functional differential equations. J. Math. Anal. Appl. 213(2), 554–572 (1997)
K.E.M. Church, X. Liu, Bifurcation analysis and application for impulsive systems with delayed impulses. Int. J. Bifurcation Chaos 27(12), 1750186 (2017)
K.E.M. Church, X. Liu, Computation of centre manifolds and some codimension-one bifurcations for impulsive delay differential equations. J. Differ. Equ. 267(6), 3852–3921 (2019)
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Church, K.E.M., Liu, X. (2021). Computational Aspects of Centre Manifolds. In: Bifurcation Theory of Impulsive Dynamical Systems. IFSR International Series in Systems Science and Systems Engineering, vol 34. Springer, Cham. https://doi.org/10.1007/978-3-030-64533-5_6
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DOI: https://doi.org/10.1007/978-3-030-64533-5_6
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