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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.

High codimensional bifurcation analysis to a six-neuron BAM neural network