Publications on Dynamical Systems

1. V.Kertesz and R.E.Kooij, Degenerate Hopf bifurcation in twodimensions, Journal of Nonlinear Analysis, TMA, Vol.17, No.3, 1991, 267-283.
2. R.E.Kooij and P.G.Bakker, Three-dimensional viscous flow structures from bifurcation of a degenerate singularity with three zero eigenvalues, Report LR-572, 1989, University of Technology Delft.
3. R.E.Kooij, Cubic systems with four real line invariants, Math. Proc. of the Cambridge Philosophical Society, Vol.118, No.7, 1995.
4. R.E.Kooij, Cubic systems with four line invariants, including complex conjugated lines, Differential Equations and Dynamical Systems, Vol. 4, No. 1, 1996, 43-56.
5. R.E.Kooij, Existence and uniqueness of limit cycles in quadratic systems of class (III)l=m=0, Ann.of Diff.Eqs., 7(2), 1991, 133-144.
6. R.E.Kooij, Real polynomial systems of degree n with n+1 line invariants, J.of Diff.Eqs., Vol.116, No.2, 1995, 249-264.
7. R.E.Kooij and J.W.Reyn, On the phase-plane analysis of self-similar gravity currents, Delft Progress Report 15, 1991, 21-31.
8. Wang Xian and R.E.Kooij, Limit cycles in cubic systems with a cusp, SIAM J.on Mathematical Analysis, Vol.23, no.6, 1992, 1609-1622.
9. R.E.Kooij and C.J.Christopher, Algebraic invariant curves and the integrability of polynomial systems, Applied Math. Letters, Vol.6, No.4, 1993, 51-53.
10. J.W.Reyn and R.E.Kooij, Singular points at infinity of quadratic systems of differential equations, J. of Nonlinear Analysis TMA, Vol.24, No.6, 1995, 895-927.
11. R.E.Kooij and W.T. van Horssen, Structurally stable quadratic systems without limit cycles, Ann. of Diff. Eqs., Vol.10, No.3, 1994, 259-274.
12. R.E.Kooij, Existence and uniqueness of limit cycles for a special system of differential equations on the plane, Proceedings Equadiff '91 Barcelona, World Scientific, 1993, 645-650.
13. W.T.van Horssen and R.E.Kooij, Bifurcation of limit cycles in a particular class of quadratic systems with two centers, J. of Diff. Eqs., Vol.114, No.2, 1994.
14. A.Zegeling and R.E.Kooij, Uniqueness of limit cycles in polynomial systems with algebraic invariants, Bull. of Austr. Math. Soc., Vol.49, No.1, 1994, 7-20.
15. R.E.Kooij and A.Zegeling, Qualitative properties of two-dimensional predator-prey systems, Nonlinear Analysis, TMA, Vol. 29, No. 6, 1997, 693-715.
16. R.E.Kooij and A.Zegeling, A predator-prey model with Ivlev's functional response, J. of Math. Anal. and Appl., 198, 1996, 473-489.
17. R.E.Kooij and Sun Jianhua, A note on "Uniqueness of limit cycles in Lienard type systems", J. of Math. Anal. and Appl., Vol. 208, 1997, 260-276.
18. J.C.Artes, R.E.Kooij and J.Llibre, Structurally stable quadratic vector fields, Memoires of the American Math. Society, Number 639, 1998.
19. J.W.Reyn and R.E.Kooij, Phase portraits of quadratic systems with two finite singular points, Proceedings of Symposium on Planar Nonlinear Dynamical Systems, Delft 1995, in Special Issue of Differential Equations and Dynamical Systems, ed. by R.E.Kooij and A.H.P. van der Burgh, Vol. 5, No. 3/4, 1997, 355-420.
20. R.E.Kooij, A new proof and applications of Lienard's theorem, Proceedings of New Directions in Applied Mathematics, Hyderabad, India 1996, in Special Issue of Differential Equations and Dynamical Systems, Vol. 6, No. 1/2, 1998, 87-100.
21. R.E. Kooij, A. Gasull and J. Torregrosa, Limit cycles in the Holling-Tanner model, Publicacions Matematiques, Vol. 41, 1997, 149-167.
22. Zegeling and R.E. Kooij, The distribution of limit cycles in quadratic systems with four critical points, J. of Diff. Eqs., Vol. 151, 373-385, 1999.
23. Zegeling and R.E. Kooij, Uniqueness of limit cycles in models for microparasitic and macroparasitic diseases, J. of Math. Biol., Vol. 36, 1998, 407-417.
24. R.E.Kooij and A.Zegeling, Limit cycles in quadratic systems with a weak focus and a strong focus, Kyungpook Mathematical Journal, Vl. 38, No. 2, 1998, 323-340.
25. F. Dumortier, R.E. Kooij and Li Chengzhi, Cubic Lienard systems with quadratic damping, Qual. Theory of Dyn. Systems, 1, 163-211, 2000.
26. R.E. Kooij and A. Zegeling, Co-existence of centers and limit cycles in polynomial systems, Rocky Mountain Journal of Mathematics, Vol. 30, No. 2, 2000, 621-640.
27. R.E. Kooij and F. Giannakopoulos, Periodic orbits in planar systems modeling neural activity, Quart. of Appl. Math., Vol. 58, No. 3, 2000, 437-457.