Revista Matemática Complutense

, Volume 26, Issue 1, pp 193–213

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


DOI: 10.1007/s13163-012-0099-6

Cite this article as:
Hbid, M.L., Sánchez, E. & Ouifki, R. Rev Mat Complut (2013) 26: 193. doi:10.1007/s13163-012-0099-6


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 G4 is provided.


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

Mathematics Subject Classification

34K18 34K13 37G99 

Copyright information

© 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