Integrability of a family of four-dimensional quadratic Lotka–Volterra complex systemsMastev, Ivan (Avtor) Romanovski, Valery (Avtor) integrabilitylinearizabilitynormal formstime-reversibilitypolynomial systems of ODEsThis 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.MDPI20262026-05-15 09:12:42Članek v reviji98092UDK: 51COBISS_ID: 278060803DOI: 10.3390/axioms15040297ISSN pri članku: 2075-1680sl© 2026 by the authors