Bifurcation analysis on a generalized recurrent neural network with two interconnected three-neuron components

A class of recurrent neural networks is constructed by generalizing a specific class of n-neuron networks. It is shown that the newly constructed network experiences generic pitchfork and Hopf codimension one bifurcations. It is also proved that the emergence of generic Bogdanov–Takens, pitchfork–Hopf and Hopf–Hopf codimension two, and the degenerate Bogdanov–Takens bifurcation points in the parameter space is possible due to the intersections of codimension one bifurcation curves. The occurrence of bifurcations of higher codimensions significantly increases the capability of the newly constructed recurrent neural network to learn broader families of periodic signals.

► We construct a recurrent neural network by generalizing a specific n-neuron network. ► Several codimension 1 and 2 bifurcations take place in the newly constructed network. ► The newly constructed network has higher capabilities to learn periodic signals. ► The normal form theorem is applied to investigate dynamics of the network. ► A series of bifurcation diagrams is given to support theoretical results.