Delay-induced spiking dynamics in integrate-and-fire neurons
The paper studies the time delay effect on the well-known integrate-and-fire (IF) model. The consideration on time delay leads to Hopf bifurcation and proposes a new mechanism for IF models to generate spiking dynamics. It is interesting that, under the consideration of delayed adaptation on the membrane potential, the range of parameter in IF model with spiking dynamics becomes wider and the reason is the appearance of Hopf bifurcation and the existence of an unstable orbit. And for a coupled two neuron system, different values of delay times will imply the appearance of emergence and death of spiking. In order to study the properties of Hopf bifurcation (including the direction of Hopf bifurcation and stability of the bifurcating periodic orbits), the authors apply the normal form approach and the center manifold theory to the study of delayed IF model. This provides a new idea for the research of delay system especially the study of bifurcation theory. Moreover, the study of the coupled two-neuron system shows that, different from single-neuron system, there are both emergence and death of spiking according to different ranges of parameters. This enlightens us that the coupled system has more complex dynamic behaviour than the single system, especially when the delay is introduced. In the study of delay system, the introduction of delay should be scientific and reasonable. Thus, it will be better if this paper explains the delay type of IF model in detail. In addition, compared with the local stability studied in this paper, the result of global stability is more attractive and accurate to describe the dynamic behaviour of delayed system.
scientific article; zbMATH DE number 7360348
scientific article