Electronic Journal of Qualitative Theory of Differential Equations (Jan 2000)

Hopf bifurcation of integro-differential equations

  • Alexander Domoshnitsky,
  • Ya. Goltser

DOI
https://doi.org/10.14232/ejqtde.1999.5.3
Journal volume & issue
Vol. 1999, no. 3
pp. 1 – 11

Abstract

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A method reducing integro-differential equations (IDEs) to system of ordinary ones is proposed. On this base stability and bifurcation phenomena in critical cases are studied. Analog of Hopf bifurcation for scalar IDEs of first order is obtained. Conditions of periodic solution existence are proposed. One of the conclusions is the following: phenomena characterized by two dimension systems of ODEs appear for scalar IDEs.