20.500.12556/DKUM-98092 Integrability of a family of four-dimensional quadratic Lotka–Volterra complex systems This work addresses the integrability of four-dimensional quadratic Lotka–Volterra systems exhibiting (1:−1:i:−i) resonance by identifying the parameter constraints required for such properties to exist. Our results show that, within this family, integrability is connected to linearizability and time-reversibility. To establish these results, we combine theoretical and computational methods. On the theoretical side, we use Poincaré–Dulac normal form theory and methods based on Gröbner basis theory. On the computational side, we apply the algorithms described in the paper to compute normal forms and minimal associated prime ideals required for the analysis of the integrability conditions. integrability linearizability normal forms time-reversibility polynomial systems of ODEs integrabilnost normalne oblike reverzibilnost true false true MDPI Angleški jezik Slovenski jezik https://www.mdpi.com/journal/axioms © 2026 by the authors Članek v reviji 2026-05-15 09:12:42 2026-05-15 09:12:42 2026-05-16 03:14:28 0000-00-00 00:00:00 2026 0 0 17 str. issue 4, [article no.] 297 Vol. 15 2026 0000-00-00 Zaloznikova Objavljeno NiDoloceno 2026-03-24 2026-04-17 2026-04-17 51 278060803 10.3390/axioms15040297 2075-1680 axioms-15-00297-v2.pdf axioms-15-00297-v2.pdf 1 9C31539D499FB49E4E041B7FF5BB684E 74684ae4042929d6534f6ea3cb30e1e2bf3c39f2718b4c47e03d3c8ffb4fd091 cefef7f3-502d-11f1-9c27-00155d0001a1 https://dk.um.si/Dokument.php?lang=slv&id=206118 Fakulteta za elektrotehniko, računalništvo in informatiko 0 0 0