A cubic-quadratic phenomenological model explains the spiking, chaotic and bursting behaviors of neuron

In this manuscript, we present a two-dimensional phenomenological spiking neuron model. By analyzing the bifurcation diagram and phase portraits of the two-dimensional model, Andronov-Hopf bifurcation, saddle-point bifurcation and saddle-point on invariant circle bifurcation are discussed in detail. Based on the above analysis, a periodic input current is designed to simulate the basic firing mode of a single neuron. With the change of the input current frequency, the model can reproduce rich dynamical behaviors such as spike, bursts, and chaos.