Hopf bifurcations in time-delay systems with band-limited feedback

@article{Illing2005HopfBI,
  title={Hopf bifurcations in time-delay systems with band-limited feedback},
  author={L. Illing and D. Gauthier},
  journal={Physica D: Nonlinear Phenomena},
  year={2005},
  volume={210},
  pages={180-202}
}
  • L. Illing, D. Gauthier
  • Published 2005
  • Physics, Mathematics
  • Physica D: Nonlinear Phenomena
  • Abstract We investigate the steady-state solution and its bifurcations in time-delay systems with band-limited feedback. This is a first step in a rigorous study concerning the effects of AC-coupled components in nonlinear devices with time-delayed feedback. We show that the steady state is globally stable for small feedback gain and that local stability is lost, generically, through a Hopf bifurcation for larger feedback gain. We provide simple criteria that determine whether the Hopf… CONTINUE READING

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