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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Bélair et al. (1994) studied this question.
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