Chaos and bursting patterns in two-neuron Hopfield neural network and analog implementation

To demonstrate and elucidate bursting patterns and their bifurcation mechanisms, a two-neuron Hopfield neural network is proposed in this paper. The proposed non-autonomous model has a time-varying equilibrium point whose stability undergoes continuous evolution in response to changes in stimulation, and exhibits chaotic dynamics, especially the quasi-periodic and periodic bursting patterns. Over a full bursting cycle, the stability evolution of the time-varying equilibrium point triggers Hopf bifurcation and fold bifurcation, leading to the emergence of quasi-periodic or periodic bursting. To elucidate the bifurcation mechanisms, the transitions between the spiking state and the resting state are demonstrated, thereby identifying the Hopf/Hopf quasi-periodic bursting and fold/fold/Hopf periodic bursting. In addition, a simple analog electronic circuit is designed for the physical implementation of the non-autonomous model, and a printed-circuit board based hardware circuit is made to test the experimental results to verify the numerical results.