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- Open Access
A complete dynamical study of time-varying and interconnected networks of pulse-coupled theta neurons
© Luke et al; licensee BioMed Central Ltd. 2013
- Published: 8 July 2013
- Bifurcation Point
- Interconnected Network
- Neuronal Excitability
- Basic Building Block
- Exact Model
In 1986, Ermentrout and Kopell[1, 2] first introduced a novel mathematical approach to describe the behavior of Type I neurons near their bifurcation point. Starting from these "theta" neurons as basic building blocks, we have developed an exact model that examined the dynamical conditions under which large-scale collective behavior emerges. In addition to being analytically solvable, one key element of our approach was the introduction of heterogeneity within the neuronal population, specifically in terms of individual neuronal excitability. We found that only three steady-state solutions can result from this model: two static equilibrium states and a class of periodic solutions, or limit cycles. Further, we completely classified the dynamical conditions under which transitions between these collective states can occur.
- Ermentrout GB, Kopell N: Parabolic bursting in an excitable system coupled with a slow oscillation. SIAM J Appl Math. 1986, 233-253. 46Google Scholar
- Ermentrout GB: Type I membranes, phase resetting curves, and synchrony. Neural Comp. 1996, 979-1001. 8Google Scholar
- Luke TB, Barreto E, So P: Complete Classification of Macroscopic Behavior for a Heterogeneous Network of Theta Neurons. submitted to Neural Comp. 2013Google Scholar
- So P, Luke TB, Barreto E: Networks of Theta Neurons with Time-Varying Excitability: Macroscopic Chaos, Multi-Stability, and Final State Uncertainty. submitted to Physica D. 2012Google Scholar
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