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.

Keywords

• learning-process
• cusp
• universal unfolding
• Bogdanov–Takens bifurcation