Delay of bifurcation phenomena and their analysis

Tuesday, October 28, 1997 - 3:45pm - 4:15pm
Keller 3-180
Jianzhong Su (Texas A & M University)
The phenomena of delay of bifurcation occur in some fast-slow problems (or simply slow passage problems) where a parameter is slowly changing resulting in changes of static stability. The solutions of the equation ($varepsilon$ $neq$ 0 ) actually follow the unstable singular solution ($varepsilon$ = 0 )until some integral conditions are satisfied. We consider several interesting cases including the FitzHugh-Nagumo Equation, FHN model with periodic forcing and particularly a system with one simple eigenvalue which slowly passes zero.