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Atamanyk, J. and Langford, W.F. (2003) A Compartmental Model of Cheyne-Stokes Respiration. In: Ruan, S., Wolkowicz, G.S.K. and Wu, J., Eds., Dynamical Systems and Their Applications in Biology (Fields Institute Communications Volume 36), American Mathematical Society, Providence, 1-16.

has been cited by the following article:

• TITLE: Evaluation of Kinetic Properties of Dendritic Potassium Current in Ghostbursting Model of Electrosensory Neurons

  AUTHORS: Takaaki Shirahata

  KEYWORDS: Mathematical Model, Bifurcation, Ghostbursting, Time Constant

  JOURNAL NAME: Applied Mathematics, Vol.6 No.1, January 12, 2015

  ABSTRACT: A ghostbursting model is a mathematical model (a system of coupled nonlinear ordinary differential equations) that is based on the Hodgkin-Huxley formalism. The ghostbursting model describes bursting similar to the in vitro bursting of electrosensory neurons of weakly electric fish. Doiron and coworkers have focused on two system parameters of the model: maximal conductance of the dendritic potassium current and the current injected into the somatic compartment . They performed bifurcation analysis and revealed that the -parameter space was divided into three dynamical states: quiescence, periodic tonic spiking, and bursting. The present study focused on a third system parameter: the time constant of dendritic potassium current inactivation . A computer simulation of the model revealed how the dynamical states of the -parameter space changed in response to variations of .