A modified radial isochron clock with slow and fast dynamics as a model of pacemaker neurons. Global bifurcation structure when driven by periodic pulse trains.
A simple mathematical model of living pacemaker neurons is proposed. The model has a unit circle limit cycle and radial isochrons, and the state point moves slowly in one region and fast in the remaining region; regions can correspond to the subthreshold activity and to the action potentials of pacemaker neurons, respectively. The global bifurcation structure when driven by periodic pulse trains was investigated using one-dimensional maps (PTC), two-dimensional bifurcation diagrams, and skeletons involving stimulus period and intensity. The existence of both the slow and the fast dynamics has a critical influence on the global bifurcation structure of the oscillator when stimulated periodically.
Nomura
T
T
Department of Biophysical Engineering, Faculty of Science, Osaka University, Japan.
Sato
S
S
Doi
S
S
Segundo
J P
JP
Stiber
M D
MD
D001683:Biological Clocks; D003198:Computer Simulation; D003491:Cybernetics / Q000379:methods*; D008954:Models, Biological; D009474:Neurons / Q000502:physiology*