Journal of Dynamics and Differential Equations

, Volume 7, Issue 1, pp 213–236 | Cite as

Limit cycles, tori, and complex dynamics in a second-order differential equation with delayed negative feedback

  • Sue Ann Campbell
  • Jacques Bélair
  • Toru Ohira
  • John Milton


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.

Key words

Time delay negative feedback Hopf bifurcations center manifold invariant tori 

AMS(MOS) classification numbers

34K15 54F36 93D15 


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Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • Sue Ann Campbell
    • 1
    • 2
    • 3
  • Jacques Bélair
    • 1
    • 3
    • 6
  • Toru Ohira
    • 4
  • John Milton
    • 1
    • 5
  1. 1.Centre for Nonlinear Dynamics in Physiology and MedicineMcGill UniversityMontréalCanada
  2. 2.Department of Mathematics and StatisticsConcordia UniversityMontréalCanada
  3. 3.Centre de recherches mathématiquesUniversité de MontréalMontréalCanada
  4. 4.Department of PhysicsThe University of ChicagoChicago
  5. 5.Department of NeurologyThe University of ChicagoChicago
  6. 6.Département de mathématiques et de statistiqueUniversité de MontréalMontréalCanada

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