doi: 10.7763/IJAPM.2013.V3.188
Bifurcation Analysis in a Neuronal Model without/with Delay
Shyan-Shiou Chen
- the Department of Mathematics, National Taiwan Normal University, Taipei, Taiwan
Abstract
In this study, we provide a global picture of the bifurcation scenario of a two-dimensional Hindmarsh-Rose (HR) type model. We present all of the possible classifications based on the following results: first, the number and stability of the equilibrium are analyzed in detail with a table built to show not only how to change the stability of the equilibrium but also which two equilibria collapse through the saddle-node bifurcation; secondly, sufficient conditions for an Andronov-Hopf bifurcation and a saddle-node bifurcation are mathematically confirmed; and finally, we provide sufficient conditions for a Bogdanov-Takens (BT) bifurcation and a Bautin bifurcation. Finally, we present characteristic equation for the HR type model with delay. These results provide us a diversity of behaviors for the model. The results in the paper should be helpful when choosing suitable parameters for fitting experimental observations.
Keywords
- Two-dimensional hindmarsh-rose type model
- bifurcations
How to Cite
Shyan-Shiou Chen, "Bifurcation Analysis in a Neuronal Model without/with Delay," International Journal of Applied Physics and Mathematics, vol. 3, no. 2, pp. 117-122, 2013. https://doi.org/ 10.7763/IJAPM.2013.V3.188
Copyright & License
Copyright © 2013 by the authors. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).