Bifurcations of emergent bursting in a neuronal network.
Bottom Line:
Here we present a general approach to mathematically tackle a complex neuronal network so that we can fully understand the underlying mechanisms.The approach enables us to uncover how emergent synchronous bursting can arise from a neuronal network which embodies known biological features.Surprisingly, the bursting mechanisms are similar to those found in other systems reported in the literature, and illustrate a generic way to exhibit emergent and multiple time scale oscillations at the membrane potential level and the firing rate level.
View Article:
PubMed Central - PubMed
Affiliation: Centre for Computational Systems Biology and School of Mathematical Sciences, Fudan University, Shanghai, China.
ABSTRACT
Show MeSH
Complex neuronal networks are an important tool to help explain paradoxical phenomena observed in biological recordings. Here we present a general approach to mathematically tackle a complex neuronal network so that we can fully understand the underlying mechanisms. Using a previously developed network model of the milk-ejection reflex in oxytocin cells, we show how we can reduce a complex model with many variables and complex network topologies to a tractable model with two variables, while retaining all key qualitative features of the original model. The approach enables us to uncover how emergent synchronous bursting can arise from a neuronal network which embodies known biological features. Surprisingly, the bursting mechanisms are similar to those found in other systems reported in the literature, and illustrate a generic way to exhibit emergent and multiple time scale oscillations at the membrane potential level and the firing rate level. |
Related In:
Results -
Collection
getmorefigures.php?uid=PMC3369873&req=5
Mentions: Interestingly, aside from the above two bifurcations, the other two bifurcations appear almost symmetrically and consecutively. When passes through Hz, the other subcritical Hopf bifurcation of the system (8) emerges with a positive FLC, (0.6262), which changes the stability of the originally-unstable equilibrium and brings an unstable limit cycle (Fig. 5F–G). Moreover, the amplitude of the bifurcated unstable limit cycle grows until increasingly approaches Hz, where the other saddle-node bifurcation occurs. This bifurcation leads to the coalescence and annihilation of the two limit cycles (Fig. 5H–I). The above-expatiated bifurcation procedure of the system (8) is illustrated in Fig. 7A. |
View Article: PubMed Central - PubMed
Affiliation: Centre for Computational Systems Biology and School of Mathematical Sciences, Fudan University, Shanghai, China.