On the integrability of persistent quadratic three-dimensional systemsFerčec, Brigita (Avtor) Žulj, Maja (Avtor) Mencinger, Matej (Avtor) ordinary differential equationsthree-dimensional systemsintegrability problempersistent systemsWe consider a nine-parameter familiy of 3D quadratic systems, x˙ = x + P2(x, y, z), y˙ = −y + Q2(x, y, z), z˙ = −z + R2(x, y, z), where P2, Q2, R2 are quadratic polynomials, in terms of integrability. We find necessary and sufficient conditions for the existence of two independent first integrals of corresponding semi-persistent, weakly persistent, and persistent systems. Unlike some of the earlier works, which primarily focus on planar systems, our research covers three-dimensional spaces, offering new insights into the complex dynamics that are not typically apparent in lower dimensions.MDPI20242024-05-23 15:32:20Članek v reviji88769UDK: 517.91COBISS_ID: 196478979DOI: 10.3390/math12091338ISSN pri članku: 2227-7390sl© 2024 by the authors