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.
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Campbell, S.A., Bélair, J., Ohira, T. et al. Limit cycles, tori, and complex dynamics in a second-order differential equation with delayed negative feedback. J Dyn Diff Equat 7, 213–236 (1995). https://doi.org/10.1007/BF02218819
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DOI: https://doi.org/10.1007/BF02218819