Firing properties of single neurons in the nervous system have been recognized to be determined by their intrinsic ion channel dynamics and extrinsic synaptic inputs. Previous studies have suggested that dendritic structures exhibit significant roles in the modulation of somatic firing behavior in neurons. Following these studies, we show that finite information transmission delay between dendrite and soma can also influence the somatic firings in neurons. Our investigation is based on a two-compartment model which can approximately reproduce the firing activity of cortical pyramidal neurons. The obtained simulation results indicate that under subthreshold stimulus, spontaneous fast spiking activity is induced by large values of time delay, while for suprathreshold stimulus, regular bursting, chaotic firing and fast spiking can be observed under different time delays. More importantly, the transition mode between these diverse firing patterns with the variation of delay shows a period-doubling phenomenon under certain stimulus intensity. Consequently, our model results can not only illustrate the influential roles of internal time delay in the generation of a diversity of neuronal firing patterns, but also provide us with frameworks for investigating the impacts of internal time delay on the firing properties of many other neurons in the nervous system.
We have studied the role of external current stimuli in a four-dimensional Hodgkin-Huxley-type model of cold receptor in this paper. Firstly, we researched its firing patterns from direct current (DC) and alternating current (AC) stimuli. Under different values of DC stimulus intensity, interspike intervals (ISIs) with period-doubling bifurcation phenomena appeared. Second, research has shown that neurons are extremely sensitive to changes in the frequency and amplitude of the current used to stimulate them. As the stimulus frequency increased, discharge rhythms emerged ranging from burst firing to chaotic firing and spiking firing. Meanwhile, various phase-locking patterns have been studied in this paper, such as p : 1 (p > 1), 1 : q (q > 1), 2 : q (q > 1) and p : q (p; q > 1), etc. Finally, based on the fast-slow dynamics analysis, codimension-two bifurcation analysis of the fast subsystem was performed in the parameter (asr;B)-plane. We mainly investigated cusp bifurcation, fold-Hopf bifurcation, Bogdanov-Takens bifurcation and generalized Hopf bifurcation. These results revealed the effect of external current stimuli on the neuronal discharge rhythm and were instructive for further understanding the dynamical properties and mechanisms of the Huber-Braun model.