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Article . 2023 . Peer-reviewed
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Bogdanov–Takens Bifurcation Analysis of a Learning-Process Model

descriptionPublicationkeyboard_double_arrow_right Article 31 Aug 2023 English Publisher:MDPI AGJournal:Axioms, volume 12, page 853 (eissn: 2075-1680, Copyright policy )
Authors: Zhenliang Zhu; Yuxian Guan;

doi: 10.3390/axioms12090853

Bogdanov–Takens Bifurcation Analysis of a Learning-Process Model

Abstract

In this paper, as a complement to the works by Monterio and Notargiacomo, we analyze the dynamical behavior of a learning-process model in a case where the system admits a unique interior degenerate equilibrium. Meanwhile, we acquire the sufficient condition for the cusp of codimension 2 and verify that the system undergoes Bogdanov–Takens bifurcation around the cusp. Finally, we give a numerical simulation to support the theoretical results.

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Keywords

Bogdanov–Takens bifurcation, universal unfolding, learning-process, QA1-939, cusp, Mathematics

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
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