posted on 2005-07-25, 13:03authored byMatthew G. Denman-Johnson, S. Coombes
The McKean model of a neuron possesses a one dimensional fast voltage-like variable and a slow
recovery variable. A recent geometric analysis of the singularly perturbed system has allowed an
explicit construction of its phase response curve [S Coombes 2001 Phase-locking in networks of
synaptically coupled McKean relaxation oscillators, Physica D, Vol 160, 173-188]. Here we use
tools from coupled oscillator theory to study weakly coupled networks of McKean neurons. Using
numerical techniques we show that the McKean system has traveling wave phase-locked solutions
consistent with that of a network of more biophysically detailed Hodgkin-Huxley neurons.
History
School
Science
Department
Mathematical Sciences
Pages
232927 bytes
Publication date
2003
Notes
This pre-print has been submitted, and accepted, to the journal, Physical Review E. The definitive version: DENMAN-JOHNSON, M. and COOMBES, S.,2003. A continuum of weakly coupled oscillatory McKean neurons. Physical Review E, 67(5), art. no. 051903 is available online at http://pre.aps.org/.