Search results for: UNIMODAL MAPS

• Dynamics of S-unimodal maps used in population modeling.

  Open Research Data

  open access

  • Z. Kontna
  • J. Signerska-Rynkowska
  • G. Graff

  S-unimodal maps are maps of the interval with negative Schwarzian derivative and having only one turning point (such that the map is increasing to the left of the turning point and decreasing to the right of it). Theory of S-unimodal maps is now a well-developed branch of discrete dynamical systems, including famous Singer theorem which implies existence...

• Wild oscillations in a nonlinear neuron model with resets: (I) Bursting, spike-adding and chaos

  Publication

  • J. Rubin
  • J. Signerska-Rynkowska
  • J. Touboul
  • A. Vidal

  - DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B - Year 2017

  In a series of two papers, we investigate the mechanisms by which complex oscillations are generated in a class of nonlinear dynamical systems with resets modeling the voltage and adaptation of neurons. This first paper presents mathematical analysis showing that the system can support bursts of any period as a function of model parameters, and that these are organized in a period-incrementing structure. In continuous dynamical...

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