Global multistability and analog circuit implementation of an adapting synapse-based neuron model

Generally, neural networks involve the change with time of the neuron activities and that in strength of the synapses between neurons. This paper investigates the global multistability and analog circuit implementation of a two-dimensional adapting synapse-based neuron model in depth. The neuron model is non-autonomous and possesses periodically switchable equilibrium states associated with the externally imposed input closely. In every full periodic cycle of the input, the equilibrium stability has complex dynamical transitions between stable and unstable points via Hopf/fold bifurcations, resulting in the emergence of the global multistability that was not yet reported previously. Complex dynamics of the global coexisting multiple firing activities are demonstrated by multiple numerical measures, such as bifurcation plot, dynamical map, phase plane plot, and basin of attraction. Furthermore, an off-the-shelf discrete component-based circuit design is optimized to implement the neuron model and the outputs agree with the numerical results well.