Do the Complex Fixed Points of the Morris-Lecar System Have a Slowing Down Effect?

Karmarkar, Vivek N (2017) Do the Complex Fixed Points of the Morris-Lecar System Have a Slowing Down Effect? Masters thesis, Indian Institute of Science Education and Research Kolkata.

PDF (MS dissertation of Vivek N Karmarkar (11MS075)) VNK_11MS075.pdf - Submitted Version Restricted to Repository staff only Download (3MB)

Abstract

The Morris-Lecar model is one of the most popular models in computational neuroscience. It was born in relation to an experiment carried out on the giant barnacle muscle fiber. This model has the property of simultaneous existence of a limit cycle and complex fixed points, born out of a saddle-node bifurcation. The slowing down effect due to the remnant of the saddle-node bifurcation called the saddle-node ghost has been studied by Strogatz in a simple model related to the synchronous flashing of fireflies. In this thesis, we have developed a toy-model system of the Morris-Lecar model with the same dynamical characteristics as the original Morris-Lecar system. After mathematically defining a saddle-node ghost in relation to the complex fixed points, we have attempted to investigate the connection between a slowing down on the limit cycle and such a ghost fixed point. We have described the effect of the ghost fixed as an inequality expressed in terms of a scaled distance between two special points of the system. This analysis has been repeated for the original Morris-Lecar model.

Actions (login required)

View Item