Abstract
Noticeable in two-parameter bifurcation diagrams for several neural models is the juxtaposition of cusps and Bogdanov–Takens points. We find parameters for Morris–Lecar and Hodgkin–Huxley models where the two bifurcations merge at a degenerate Bogdanov–Takens-cusp codimension three bifurcation that has been analyzed by Guckenheimer (1986) and Dumortier et al. (1991). This rich singularity has an unfolding as a simple second-order cubic dynamical system which can be used for modeling and analysis. We argue the importance and discuss consequences of this bifurcation as a minimal organizing center for two-dimensional type I excitable membranes.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
