Linear Stability and Bifurcation Analysis

Chapter
Part of the Springer Series in Synergetics book series (SSSYN)

Abstract

In our study of DDEs, we will mainly concentrate on equations with constant time delay (single or multiple). In particular considering Eq. (1.3), in this chapter we will consider scalar DDEs (n = 1 in Eq. (1.2)) and analyse the linear stability and bifurcation aspects of a class of such equations. We will use the usual method of infinitesimally displacing the solution around the equilibrium point, a geometric approach, and a more general approach to determine linear stability of equilibrium points and then illustrate them with specific examples. We will also point out the extension of these analyses to coupled DDEs/complex scalar equations.

References

  1. 1.
    N. McDonald, Biological Delay Systems: Linear Stability Theory (Cambridge University Press, Cambridge, 1989)Google Scholar
  2. 2.
    D.V. Ramana Reddy, Ph. D. Thesis entitled Collective Dynamics of Delay Coupled Oscillators (Institute for Plasma Research, Gandhinagar, India, 2000)Google Scholar
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    D.V. Ramana Reddy, A. Sen, G.L. Johnston, Phys. Rev. Lett. 80, 5109 (1998)ADSCrossRefGoogle Scholar
  4. 4.
    H. Niu, J. Geng, Nonlinearity 20, 2499 (2007)MathSciNetADSMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Centre for Nonlinear Dynamics, Bharathidasan UniversityTiruchirapalliIndia
  2. 2.Transdisciplinary Concepts and Methods, Potsdam Institute for Climate Impact ResearchPotsdamGermany

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