Hopf bifurcation of integro-differential equations

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A method reducing integro-differential equations (IDE's) to systems of ordinary differential equations is proposed. Stability and bifurcation phenomena in critical cases are studied using this method. An analog of Hopf bifurcation for scalar IDE's of first order is obtained. Conditions for existence of periodic solution are proposed. We conclude that phenomena typical for two dimensional systems of ODE's appear for scalar IDE's.

Original languageEnglish
Pages (from-to)1-11
Number of pages11
JournalElectronic Journal of Qualitative Theory of Differential Equations
StatePublished - 2000


  • Bifurcation
  • Integral equations
  • Periodic solution
  • Stability


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