Stability and Hopf bifurcation analysis of a pair of three-neuron loops with time delays

This paper reveals the dynamical behaviors of a neural network consisting of a pair of bidirectional loops each with three identical neurons and two-way couplings between neurons of each individual loop. Time delays are introduced not only in the couplings between the loops but also in the internal connections within the individual loops. The study derives the conditions for the local stability of the network equilibrium and the existence of Hopf bifurcation. Afterwards, the study turns to showing the rich dynamical behaviors of the network through numerical analysis, such as multiple stability switches of network equilibrium, synchronous/asynchronous periodic oscillations, and the coexistence of bifurcated solutions.