Stech, Harlan W. Generic Hopf bifurcation in a class of integro-differential equations. (English) Zbl 0756.45017 J. Integral Equations Appl. 3, No. 1, 175-193 (1991). The author studies the Hopf bifurcation problem for a certain type of functional differential equations, deriving a so-called normal form equation that determines the behaviour of generic bifurcations. Computational aspects of the problem are also illustrated by means of examples. Reviewer: C.Constanda (Glasgow) Cited in 2 Documents MSC: 45J05 Integro-ordinary differential equations 45G10 Other nonlinear integral equations 65R20 Numerical methods for integral equations Keywords:nonlinear perturbations; neutral stability curve; Hopf bifurcation; functional differential equations; normal form equation PDFBibTeX XMLCite \textit{H. W. Stech}, J. Integral Equations Appl. 3, No. 1, 175--193 (1991; Zbl 0756.45017) Full Text: DOI References: [1] J. Franke, Symbolic Hopf bifurcation calculations for functional differential equations , Master’s Thesis, University of Minnesota, June, 1989. [2] ——– and H. Stech, Extensions of an algorithm for the analysis of nongeneric Hopf bifurcations, with applications to delay-difference equations , · Zbl 0739.34032 [3] J.K. Hale, Functional differential equations , Appl. Math. Sci. Vol. 3, Springer-Verlag, New York, 1971. · Zbl 0222.34003 [4] K.B. Hannsgen, Indirect abelian theorems and a linear volterra equation , Trans. Amer. Math. Soc. 142 (1969), 539-555. JSTOR: · Zbl 0185.35801 · doi:10.2307/1995370 [5] H.W. Hethcote, H.W. Stech, and P. van den Driessche, Nonlinear oscillations in epidemic models , SIAM J. Appl. Math 1 (1981), 1-9. · Zbl 0469.92012 · doi:10.1137/0140001 [6] J.J. Levin and J. Nohel, On a nonlinear delay equation , J. Math. Anal. Appl., 8 (1964), 31-44. · Zbl 0129.07703 · doi:10.1016/0022-247X(64)90080-0 [7] H. Stech, The effect of time lags on the stability of the equilibrium solution of a nonlinear integral equation , J. Math. Biol. 5 (1978), 115-130. · Zbl 0372.92015 · doi:10.1007/BF00275894 [8] ——–, The Hopf bifurcation: A stability result and application , J. Math. Anal. Appl. 2 (1979), 525-546. · Zbl 0418.34073 · doi:10.1016/0022-247X(79)90207-5 [9] ——–, Hopf bifurcation calculations for functional differential equations , J. Math. Anal. Appl. 109 (1985), 472-491. · Zbl 0592.34048 · doi:10.1016/0022-247X(85)90163-5 [10] ——–, Nongeneric Hopf bifurcations in functional differential equations , SIAM J. Appl. Math. 16 (1985), 1134-1151. · Zbl 0586.34060 · doi:10.1137/0516084 [11] ——– and M. Williams, Stability in a class of epidemic models with delay , J. Math. Biol. 11 (1981), 95-103. · Zbl 0449.92022 · doi:10.1007/BF00275827 [12] H.O. Walther, On a transcendental equation in the stability analysis of a population growth model , J. Math. Biol. 3 (1976), 187-195. · Zbl 0339.92009 · doi:10.1007/BF00276205 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.