Revista Matemática Complutense

, Volume 26, Issue 1, pp 193–213 | Cite as

Hopf bifurcation via the Poincaré procedure in delay-differential equations with two delays

  • M. L. Hbid
  • E. Sánchez
  • R. Ouifki


In this work we apply the theory of h-asymptotic stability related to the Poincaré procedure to establish sufficient conditions for the existence of a Hopf bifurcation for a delayed differential equation with two constant delays, considering one of the delays as a parameter. An explicit calculation of the Poincaré constant G 4 is provided.


Two-delay differential equation Hopf bifurcation h-Asymptotic stability Poincaré constant 

Mathematics Subject Classification

34K18 34K13 37G99 



E. Sánchez has been supported by Ministerio de Ciencia e Innovación (Spain) Proyecto MTM2011-24321.


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© Revista Matemática Complutense 2012

Authors and Affiliations

  1. 1.Laboratoire de Mathématiques et Dynamique des Populations, Faculté des Sciences, Université Cadi AyyadUMI-UMMISCO (IRD-UPMC), Unité Associée au CNRST (URAC02)MarrakechMorocco
  2. 2.Dpto. Matemática AplicadaE.T.S. Ingenieros IndustrialesMadridSpain
  3. 3.DST/NRF Centre of Excellence in Epidemiological Modelling and Analysis (SACEMA)Stellenbosch UniversityStellenboschSouth Africa

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