Integrability and Non-Existence of Periodic Orbits for a Class of Kolmogorov Systems
By:
References
- [1] BELMONTE-BEITIA, J.: Existence of travelling wave solutions for a Fisher–Kolmogorov system with biomedical applications, Commun. Nonlinear Sci. Numer. Simul. 36 (2016), 14–20.10.1016/j.cnsns.2015.11.016
- [2] BENDJEDDOU, S. B. B.: Two non algebraic limit cycles of a class of polynomial differential systems with non-elementary equilibrium point, Tatra Mt. Math. Publ. 79 (2021), 33–46.
- [3] BENYOUCEF, S.: Polynomial differential systems with hyperbolic algebraic limit cycles, Electron. J. Qual. Theory Differ. Equ. 2020 (2020), 1–7.10.14232/ejqtde.2020.1.34
- [4] BUĹIČEK, M.—MÁLEK, J.: Large data analysis for Kolmogorov’s two-equation model of turbulence, Nonlinear Analysis: Real World Applications 50 (2019), 104–143.10.1016/j.nonrwa.2019.04.008
- [5] BUSSE,F.H.: Transition to turbulence via the statistical limit cycle route.In: Chaos and Order in Nature. Springer-Verlag, Berlin, 1981, pp. 36–44.
- [6] DUMORTIER, F.—LLIBRE, J.—ARTÉS, J. C.: Qualitative Theory of Planar Differential Systems. Springer-Verlag, Berlin, 2006.
- [7] HERING, R. H.: Oscillations in Lotka-Volterra systems of chemical reactions,J. Math. Chem. Journal 5 (1990), 197–202.10.1007/BF01166429
- [8] KINA, A.—BERBACHE, A.—BENDJEDDOU, A.: Integrability and limit cycles for a class of multi-parameter differential systems with unstable node point, Rend. Circ. Mat. Palermo (2) (2022), 1–10.10.1007/s12215-022-00774-3
- [9] KOLMOGOROV, A.: Sulla teoria di Volterra della lotta per lesistenza,Gi. Inst.Ital. Attuari 7 (1936), 74–80.
- [10] KUZNETSOV, Y. A.—KUZNETSOV, I. A.—KUZNETSOV, Y.: Elements of Applied Bifurcation Theory. Vol. 112. Springer-Verlag, Berlin, 1998.
- [11] LAVAL, G.—DONALD JOSEPH, X. M.—BEKEFI, G.—BERS, A.—PELLAT, R.— DELCROIX, J.-L.—KALMAN, G.: Plasma Physics. Gordon and Breach Science Publishers, 1975.
- [12] LLIBRE, J.—MARTÍNEZ, Y. P.—VALLS, C.: Limit cycles bifurcating of Kolmogorov systems in R2 and in R3, Commun. Nonlinear Sci. Numer. Simul. 91, (2020), Article ID 105401, 10 p.
- [13] LLIBRE, J.—SALHI, T.: On the dynamics of a class of Kolmogorov systems, Appl. Math. Comput. 225 (2013), 242–245.
- [14] LOTKA, A. J.: Science Progress in the Twentieth Century (1919-1933), Elements of Physical Biology 21 (1926), 341–343.
- [15] RAFIKOV, M.—BALTHAZAR, J. M.—VON BREMEN, H.: Mathematical modeling and control of population systems: applications in biological pest control, Appl. Math. Comput. 200, (2008), no. 2, 557–573.
- [16] SOLOMON, S.—RICHMOND, P.: Stable power laws in variable economies; Lotka-Volterra implies Pareto-Zipf, The European Physical Journal B - Condensed Matter and Complex Systems 27 (2002), 257–261.
- [17] VOLTERRA, V.: Variazioni e fluttuazioni del numero d’individui in specie animali conviventi.Società anonima tipografica “Leonardo da Vinci”, 1926.
- [18] YE, YAN QIAN—CAI, SUI LIN—CHEN, LAN SUN—HUANG, KE CHENG— LUO, DING JUN—MA, ZHI EN—WANG, ER NIAN—WANG, MING SHU— YANG, XIN AN: Theory of Limit Cycles. (Translated from the Chinese by Chi Y. Lo.) 2nd edition. Translations of Mathematical Monographs, Vol. 66. Amer. Math. Soc., Providence, RI, 1986.
Language: English
Page range: 145 - 154
Submitted on: Jul 18, 2022
Published on: Nov 29, 2022
Published by: Slovak Academy of Sciences, Mathematical Institute
In partnership with: Paradigm Publishing Services
Publication frequency: 3 times per year
Related subjects:
© 2022 Sarbast Hussein, Tayeb Salhi, Bo Huang, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.