AI Article Synopsis
- The text discusses two main patterns of neuronal activity: rapid spiking and alternating spiking with quiescence known as bursting.
- It explores how the transition from spiking to bursting in computational neuronal models involves complex structures called torus canards, which can occur in various well-known models.
- The findings suggest that torus canards are a common mechanism that separates spiking from bursting activity, highlighting their significance in understanding neuronal dynamics.
Article Abstract
Rapid action potential generation - spiking - and alternating intervals of spiking and quiescence - bursting - are two dynamic patterns commonly observed in neuronal activity. In computational models of neuronal systems, the transition from spiking to bursting often exhibits complex bifurcation structure. One type of transition involves the torus canard, which we show arises in a broad array of well-known computational neuronal models with three different classes of bursting dynamics: sub-Hopf/fold cycle bursting, circle/fold cycle bursting, and fold/fold cycle bursting. The essential features that these models share are multiple time scales leading naturally to decomposition into slow and fast systems, a saddle-node of periodic orbits in the fast system, and a torus bifurcation in the full system. We show that the transition from spiking to bursting in each model system is given by an explosion of torus canards. Based on these examples, as well as on emerging theory, we propose that torus canards are a common dynamic phenomenon separating the regimes of spiking and bursting activity.
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| http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3496470 | PMC |
| http://dx.doi.org/10.1186/2190-8567-2-3 | DOI Listing |
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