| dc.contributor.author | Goodell, Brandon Grae | |
| dc.description.abstract | A bifurcation portrait classifies the behavior of a dynamical system and how it transitions between different behaviors. A hybrid dynamical system displays both continuous and discrete dynamics and may display nonsmooth bifurcations. Herein, we analyze a novel hybrid model of a spiking neuron proposed by E.M. Izhikevich [9] that is based on a previous hybrid model with a convex spike-activation function f(x), but modified with a conductance reversal potential term. We analyze the model proposed by Izhikevich and obtain a bifurcation portrait for the continuous dynamics for an arbitrary convex spike activation function f(x). Both subcritical and supercritical Andronov-Hopf bifurcations are possible, and we numerically confirm the presence of a Bautin bifurcation for a particular choice of spike activation function. The model is capable of simulating common cortical neuron types and presents several possibilities for generalizations that may be capable of more complicated behavior. | en_US |
| dc.publisher | North Dakota State University | en_US |
| dc.rights | NDSU Policy 190.6.2 | |
| dc.title | Bifurcation Portrait of a Hybrid Spiking Neuron Model | en_US |
| dc.type | Thesis | en_US |
| dc.date.accessioned | 2017-10-20T18:11:13Z | |
| dc.date.available | 2017-10-20T18:11:13Z | |
| dc.date.issued | 2012 | |
| dc.identifier.uri | https://hdl.handle.net/10365/26666 | |
| dc.rights.uri | https://www.ndsu.edu/fileadmin/policy/190.pdf | |
| ndsu.degree | Master of Science (MS) | en_US |
| ndsu.college | Science and Mathematics | en_US |
| ndsu.department | Mathematics | en_US |
| ndsu.program | Mathematics | en_US |
| ndsu.advisor | Cope, Davis | |
