A review for dynamics in neuron and neuronal network

The biological Hodgkin-Huxley model and its simplified versions have confirmed its effectiveness for recognizing and understanding the electrical activities in neurons, and bifurcation analysis is often used to detect the mode transition in neuronal activities. Within the collective behaviors of neurons, neuronal network with different topology is designed to study the synchronization behavior and spatial pattern formation. In this review, the authors give careful comments for the presented neuron models and present some open problems in this field, nonlinear analysis could be effective to further discuss these problems and some results could be helpful to give possible guidance in the field of neurodynamics.