Voir la notice de l'article provenant de la source Math-Net.Ru
@article{SEMR_2021_18_1_a21, author = {R. Chouader and S. Benyoucef and A. Bendjeddou}, title = {Kolmogorov differential systems with prescribed algebraic limit cycles}, journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a}, pages = {1--8}, publisher = {mathdoc}, volume = {18}, number = {1}, year = {2021}, language = {en}, url = {http://geodesic.mathdoc.fr/item/SEMR_2021_18_1_a21/} }
TY - JOUR AU - R. Chouader AU - S. Benyoucef AU - A. Bendjeddou TI - Kolmogorov differential systems with prescribed algebraic limit cycles JO - Sibirskie èlektronnye matematičeskie izvestiâ PY - 2021 SP - 1 EP - 8 VL - 18 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/SEMR_2021_18_1_a21/ LA - en ID - SEMR_2021_18_1_a21 ER -
%0 Journal Article %A R. Chouader %A S. Benyoucef %A A. Bendjeddou %T Kolmogorov differential systems with prescribed algebraic limit cycles %J Sibirskie èlektronnye matematičeskie izvestiâ %D 2021 %P 1-8 %V 18 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/SEMR_2021_18_1_a21/ %G en %F SEMR_2021_18_1_a21
R. Chouader; S. Benyoucef; A. Bendjeddou. Kolmogorov differential systems with prescribed algebraic limit cycles. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 1, pp. 1-8. http://geodesic.mathdoc.fr/item/SEMR_2021_18_1_a21/
[1] A. Bendjeddou, R. Cheurfa, “On the exact limit cycle for some class of planar differential systems”, Nonlinear Differ. Equ. Appl., 14:5-6 (2007), 491–498 | Zbl
[2] A. Bendjeddou, A Berbache, R. Cherfa, “A class of Kolmogorov system with exact algebraic limit cycle”, Int. J. Differ. Equ. Appl., 14:3 (2015), 159–165 | Zbl
[3] Salah Benyoucef, “Polynomial differential systems with hyperbolic algebraic limit cycles”, Electron. J. Qual. Theory Differ. Equ., 2020, 34, 1–7 | Zbl
[4] Salah Benyoucef, Ahmed Bendjeddou, “Kolmogorov system with explicit hyperbolic limit cycle”, J. Siberian. Fed. Uni. Maths Phys., 10:2 (2017), 216–222
[5] R. Boukoucha, A. Bendjeddou, “On the dynamics of a class of rational Kolmogorov systems”, J. Nonlinear Math. Phys., 23:1 (2016), 21–27 | Zbl
[6] C. Christopher, “Polynomial vector fields with prescribed algebraic limit cycles”, Geom. Dedicata, 88:1-3 (201), 255–258 | Zbl
[7] F. Dumortier, J. Llibre, J. Artés, Qualitative theory of planar differential systems, Universitex, Springer, Berlin, 2006 | Zbl
[8] H. Giacomini, M. Grau, “On the stability of limit cycles for planar differential systems”, J. Diff. Equ., 213:2 (2005), 368–388 | Zbl
[9] H. Giacomini, J. Llibre, M. Viano, “On the nonexistence, existence and uniqueness of limit cycles”, Nonlinearity, 9:2 (1996), 501–516 | Zbl
[10] X.C. Huang, Lemin Zhu, “Limit cycles in a general Kolmogorov model”, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods, 60:8 (2005), 1393–1414 | Zbl
[11] J. Llibre, R. Ramirez, Inverse problems in ordinary differentials equation and applications, Progress in Mathematics, 313, Springer, Basel, 2016 | Zbl
[12] J. Llibre, T. Salhi, “On the dynamics of a class of Kolmogorov systems”, App. Math. Comput., 225 (2013), 242–245 | Zbl
[13] Jaume Llibre, Xiang Zhang, “A survey on algebraic and explicit non-algebraic limit cycles in planar differential systems”, Expositiones Mathematicae, 39:1 (2020), 48–61 | DOI
[14] N.G. Lloyd, J.M. Pearson, E Sáez, I. Szántó, “Limit cycles of a cubic Kolmogorov system”, Appl. Math. Lett., 9:1 (1996), 15–18 | Zbl
[15] N.G. Lloyd, J.M. Pearson, E. Sáez, I. Szántó, “A cubic Kolmogorov system with six limit cycles”, Comput. Math. Appl., 44:3-4 (2002), 445–455 | Zbl
[16] R.M. May, “Limit cycles in predator-prey communities”, Science, 177 (1972), 900–902
[17] L. Perko, Differential equations and dynamical systems, Texts in applied mathematics, 7, Third edition, Springer-Verlag, New York, 2006
[18] X. Zhang, “The 16th Hilbert problem on algebraic limit cycles”, J. Differ. Equations, 251:7 (2011), 1778–1789 | Zbl