ISSN:
1572-9222
Keywords:
Time delay
;
negative feedback
;
Hopf bifurcations
;
center manifold
;
invariant tori
;
34K15
;
54F36
;
93D15
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract We analyze a second-order, nonlinear delay-differential equation with negative feedback. The characteristic equation for the linear stability of the equilibrium is completely solved, as a function of two parameters describing the strength of the feedback and the damping in the autonomous system. The bifurcations occurring as the linear stability is lost are investigated by the construction of a center manifold: The nature of Hopf bifurcations and more degenerate, higher-codimension bifurcations are explicitly determined.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02218819