Delay-induced spiking dynamics in integrate-and-fire neurons

Experiments showed that a neuron can fire when its membrane potential (an intrinsic quality related to electrical charge) reaches specific threshold. On theoretical studies, there are two crucial issues in exploring cortical neuronal dynamics: (i) what model describes spiking dynamics of each neuron, and (ii) how the neurons connected [E. M. Izhikevich, IEEE Trans. Neural Networks, 15 (2004)]. To study first issue, we propose time delay effect on well-known integrate-and-fire (IF) which is classically introduced behaviors neural systems by using spike-and-reset procedure. Under consideration delayed adaptation potential, parameter range for IF with becomes wider due undergoing subcritical Hopf bifurcation existence an unstable orbit. second consider system coupled identical units where takes place coupling structure. We also demonstrate large enough, it contributes original viewpoint connection between neurons. In contrast emergence delay-induced single-neuron system, two-neuron involve both death according different values times. discuss ranges parameters allows occurrence behaviors.