publication . Other literature type . Preprint . Part of book or chapter of book . Article . 2013

Voltage Interval Mappings for an Elliptic Bursting Model

Jeremy Wojcik; Andrey Shilnikov;
English
  • Published: 19 Oct 2013
  • Publisher: Unpublished
Abstract
Abstract We performed a thorough bifurcation analysis of a mathematical elliptic bursting model, using a computer-assisted reduction to equationless, one-dimensional Poincare mappings for a voltage interval. Using the interval mappings, we were able to examine in detail the bifurcations that underlie the complex activity transitions between: tonic spiking and bursting, bursting and mixed-mode oscillations, and finally mixed-mode oscillations and quiescence in the FitzHugh–Nagumo–Rinzel model. We illustrate the wealth of information, qualitative and quantitative, that was derived from the Poincare mappings, for the neuronal models and for similar (electro)chemica...
Subjects
arXiv: Quantitative Biology::Neurons and CognitionAstrophysics::High Energy Astrophysical Phenomena
free text keywords: Nonlinear Sciences - Chaotic Dynamics, Mathematical analysis, Bursting, Oscillation, Poincaré conjecture, symbols.namesake, symbols, Lyapunov exponent, Topological entropy, Mathematics, Theta model, Hopf bifurcation, Homoclinic orbit, Statistical and Nonlinear Physics, Condensed Matter Physics, Biological neuron model, Bifurcation, Mathematical model, Voltage, Tonic (music)
Related Organizations
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publication . Other literature type . Preprint . Part of book or chapter of book . Article . 2013

Voltage Interval Mappings for an Elliptic Bursting Model

Jeremy Wojcik; Andrey Shilnikov;