2006/03/24 by Gautam C Sethia, Abhijit Sen, Sethia, Gautam C +1
Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #nlin.CD
paper · pdf · doi:10.48550/arxiv.nlin/0603053
10 pages including 7 figures
arxiv created 2006/03/24 · arxiv updated 2009/12/01
Bursting is a periodic transition between a quiescent state and a state of repetitive spiking. The phenomenon is ubiquitous in a variety of neurophysical systems. We numerically study the dynamical properties of a normal form of subcritical Hopf oscillator (at the bifurcation point) subjected to a nonlinear feedback. This dynamical system shows an infinite-period or a saddle-node on a limit cycle (SNLC) bifurcation for certain strengths of the nonlinear feedback. When the feedback is time delayed, the bifurcation scenario changes and the limit cycle terminates through a homoclinic or a saddle separatrix loop (SSL) bifurcation. This system when close to the bifurcation point exhibits various types of bursting phenomenon when subjected to a slow periodic external stimulus of an appropriate strength. The time delay in the feedback enhances the spiking rate i.e. reduces the interspike interval in a burst and also increases the width or the duration of a burst.