Biology – Quantitative Biology – Neurons and Cognition
Scientific paper
2010-01-29
Biology
Quantitative Biology
Neurons and Cognition
"Extended abstract" published in the Joint Conference of ASCM2009 and MACIS2009, Japan, 2009
Scientific paper
Neurons are the central biological objects in understanding how the brain works. The famous Hodgkin-Huxley model, which describes how action potentials of a neuron are initiated and propagated, consists of four coupled nonlinear differential equations. Because these equations are difficult to deal with, there also exist several simplified models, of which many exhibit polynomial-like non-linearity. Examples of such models are the Fitzhugh-Nagumo (FHN) model, the Hindmarsh-Rose (HR) model, the Morris-Lecar (ML) model and the Izhikevich model. In this work, we first prescribe the biologically relevant parameter ranges for the FHN model and subsequently study the dynamical behaviour of coupled neurons on small networks of two or three nodes. To do this, we use a computational real algebraic geometry method called the Discriminant Variety (DV) method to perform the stability and bifurcation analysis of these small networks. A time series analysis of the FHN model can be found elsewhere in related work[15].
Hanan William
Mehta Dhagash
Moroz Guillaume
Pouryahya Sepanda
No associations
LandOfFree
Stability and Bifurcation Analysis of Coupled Fitzhugh-Nagumo Oscillators does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Stability and Bifurcation Analysis of Coupled Fitzhugh-Nagumo Oscillators, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Stability and Bifurcation Analysis of Coupled Fitzhugh-Nagumo Oscillators will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-677013