Stochastic hierarchical systems: excitable dynamics

Autor/innen

  • H. Leonhardt
  • M.A. Zaks
  • M. Falcke
  • L. Schimansky-Geier

Journal

  • Journal of Biological Physics

Quellenangabe

  • J Biol Phys 34 (5): 521-538

Zusammenfassung

  • We present a discrete model of stochastic excitability by a low-dimensional set of delayed integral equations governing the probability in the rest state, the excited state, and the refractory state. The process is a random walk with discrete states and nonexponential waiting time distributions, which lead to the incorporation of memory kernels in the integral equations. We extend the equations of a single unit to the system of equations for an ensemble of globally coupled oscillators, derive the mean field equations, and investigate bifurcations of steady states. Conditions of destabilization are found, which imply oscillations of the mean fields in the stochastic ensemble. The relation between the mean field equations and the paradigmatic Kuramoto model is shown.


DOI

doi:10.1007/s10867-008-9112-1