DYNAMIC TRANSITIONS OF THE FITZHUGH-NAGUMO EQUATIONS ON A FINITE DOMAIN

摘要

The main objective of this article is to study the dynamic transitions of the FitzHugh-Nagumo equations on a finite domain with the Neumann boundary conditions and with uniformly injected current. We show that when certain parameter conditions are satisfied, the system undergoes a continuous dynamic transition to a limit cycle. A mixed type transition is also found when other conditions are imposed on the parameters. The main method used here is Ma & Wang's dynamic transition theory, which can be used generally on different set-ups for the FitzHugh-Nagumo equations.