Heterogeneity exerts a repulsive force on the approaching spiral tip, and the attractive force prevents the spiral tip from unpinning from the heterogeneity once the tip has anchored electromagnetic radiation on electrical activities of neuron, energy consumption in neurons are presented. Autapse is an unusual type of synapse generated by a neuron on itself. The effect of autapse connected to a neuron is often described by using a self-feedback forcing current in a close loop, and the electric activities of neuron can be regulated by the autapse greatly. Generally, positive feedback in the autapse can excite the quiescent neuron while negative feedback often calms down the excitable neuron.

Abstract. The nervous system is composed of a large number of neurons, and the electrical activities of neurons can present multiple modes during the signal transmission between neurons by changing intrinsic bifurcation parameters or under appropriate external forcing. In this review, the dynamics for neuron, neuronal network is introduced, for example, the mode transition in electrical activity, functional role of autapse connection, bifurcation verification in biological experiments, interaction between neuron and astrocyte, noise effect, coherence resonance, pattern formation and selection in network of neurons. Finally, some open problems in this field such as electromagnetic radiation on electrical activities of neuron, energy consumption in neurons are presented.

Abstract. In this review, the dynamics for neuron, neuronal network is introduced, for example, the mode transition in electrical activity, functional role of autapse connection, bifurcation verification in biological experiments, interaction between neuron and astrocyte, noise effect, coherence resonance, pattern formation and selection in network of neurons.