title: High codimensional bifurcation analysis to a six-neuron BAM neural network.
abstract: In this article, the high codimension bifurcations of a six-neuron BAM neural network system with multiple delays are addressed. We first deduce the existence conditions under which the origin of the system is a Bogdanov-Takens singularity with multiplicities two or three. By choosing the connection coefficients as bifurcation parameters and using the formula derived from the normal form theory and the center manifold, the normal forms of Bogdanov-Takens and triple zero bifurcations are presented. Some numerical examples are shown to support our main results.
authors.affiliation: Department of Mathematics of Shanghai University, Shanghai, 200444 China.
authors.forename: Yanwei
authors.initials: Y
authors.lastname: Liu
authors.affiliation: Institute of Systems Biology, Shanghai University, Shanghai, 200444 China.
authors.forename: Shanshan
authors.initials: S
authors.lastname: Li
authors.affiliation: Department of Mathematics of Shanghai University, Shanghai, 200444 China.
authors.forename: Zengrong
authors.initials: Z
authors.lastname: Liu
authors.affiliation: Department of Mathematics of Shanghai University, Shanghai, 200444 China.
authors.forename: Ruiqi
authors.initials: R
authors.lastname: Wang
keywords: Bogdanov–Takens bifurcation; Neural networks; Triple zero bifurcation