de Jager, P. Phase portraits for quadratic systems with a higher order singularity with two zero eigenvalues. (English) Zbl 0715.34057 J. Differ. Equations 87, No. 1, 169-204 (1990). For the quadratic system of ODE with right-hand sides consisting of polynomials with real coefficients of degree 2 and with a higher order singularity having two zero eigenvalues the phase portraits are given. These phase portraits are characterized by the number, position and character of the singular points, by the number and position of periodic solutions, by the position of the separatrices and by the behaviour at infinity. Reviewer: Yu.V.Rogovchenko Cited in 6 Documents MSC: 34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations Keywords:quadratic system; phase portraits × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Andronov, A. A.; Leontovich, E. A.; Gordon, J. J.; Maier, A. G., Qualitative Theory of Second-Order Dynamic Systems, (Israel Program for Scientific Translation (1973), Wiley: Wiley New York), Jeruzalem · Zbl 0282.34022 [2] Berlinskii, A. N., Russian Translating Programme RIS 5158 (June 1969), translated by the National Lending Library for Science and Technology, Boston Spa, Yorkshire, England [3] Blows, T. R.; Lloyd, N. G., The number of limit cycles of certain polynomial differential equations, (Proc. Roy. Soc. Edinburgh Sect. A, 98 (1984)), 215-239 · Zbl 0603.34020 [4] Chicone, C.; Shafer, D. S., Separatrix and limit cycles of quadratic systems and Dulac’s theorem, Trans. Amer. Math. Soc., 278, No. 2 (1983) · Zbl 0522.58041 [5] Coppel, W. A., A survey of quadratic systems, J. Differential Equations, 2, 293-304 (1966) · Zbl 0143.11903 [6] Coppel, W. A., Quadratic systems with a degenerate critical point, Bull. Austral. Math. Soc., 38, 1-10 (1988) · Zbl 0634.34013 [7] Date; Tsumotu, Classification and analysis of two-dimensional real homogeneous quadratic differential equation systems, J. Differential Equations, 32, 311-334 (1979) · Zbl 0378.34014 [9] Newton, T. A., Two dimensional homogeneous quadratic differential systems, SIAM Rev., 20, 120-138 (1978) · Zbl 0368.34019 [11] Reyn, J. W., Phase portraits of a quadratic system of differential equations occurring freqently in applications, Nieuw Arch. Wisk. (4), No. 1 (March 1987), Deel 5 [12] Vulpe, N. I., Affine-invariant conditions for the topological discrimination of quadratic systems with a center, Differentsial’nye Uravneniya, 19, No. 3, 371-379 (1983) · Zbl 0514.34030 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.