Stability and Bifurcations of Equilibria in a Multiple-Delayed Differential Equation
Jacques Bélair, Sue Ann Campbell
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Source: Crossref
Published: Oct 1, 1994
DOI: 10.1137/s0036139993248853
Open original source ↗Source abstract
The influence of multiple negative delayed feedback loops on the stability of a single-action mechanism are considered. A characteristic equation for the linearized 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 degenerate, higher codimension bifurcations are explicitly determined.
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