A SERIES OF BIFURCATION SCENARIOS IN THE FIRING PATTERN TRANSITIONS IN AN EXPERIMENTAL NEURAL PACEMAKER

Abstract

Various bifurcation scenarios from period-1 bursting to period-1 spiking via a complex procedure were simulated in previous theoretical studies on neuronal models. The results revealed a general principle of neuronal firing pattern transitions. In this letter, three types of bifurcation scenarios with respect to extracellar calcium concentration ([ Ca ++ ] o ) were discovered in experiments on neural pacemakers. Such a series of bifurcation scenarios implied complex structure of bifurcations in the firing pattern transitions of neurons. In the two-dimensional parameter space of Chay model, three classical kinds of bifurcation scenarios with respect to the bifurcation parameter v c (the reverse potential of calcium concentration) were simulated. By the variation of the conditional parameter, λ n , the relationship among the three bifurcation scenarios was revealed. The results not only verified the existence of different bifurcation scenarios in real neuronal system, but also indicated that the differences among the bifurcation scenarios were caused by the different configuration of parameters. The physiological significance of such bifurcation structures to a deeper understanding of neural coding mechanism was also discussed.