Stability and Bifurcations of Equilibria in a Multiple-Delayed Differential Equation

Jacques Bélair, Sue Ann Campbell
1994 SIAM Journal on Applied Mathematics  
The influence of multiple negative delayed feedback loops on the stability of a single-action mechanism are considered. A characteristic equation for the linearizcd stability of the equilibrium is completely analyzed, as a function of two parameters describing a delay in one loop and a ratio of the gains in the two feedback loops. The bifurcations occurring as the linear stability is lost are analyzed by the construction of a centre manifold. In particular, the nature of Hopf and more
more » ... , higher codimension bifurcations are explicitly determined.
doi:10.1137/s0036139993248853 fatcat:p32myp2uobb3lkpazgwimgz53e