On the Integrability of Persistent Quadratic Three-Dimensional Systems

Brigita Ferčec, Maja Žulj and Matej Mencinger ()
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Brigita Ferčec: Faculty of Energy Technology, University of Maribor, Hočevarjev trg 1, SI-8270 Krško, Slovenia
Maja Žulj: Faculty of Energy Technology, University of Maribor, Hočevarjev trg 1, SI-8270 Krško, Slovenia
Matej Mencinger: Faculty of Natural Science and Mathematics, University of Maribor, Koroška Cesta 160, SI-2000 Maribor, Slovenia

Mathematics, 2024, vol. 12, issue 9, 1-12

Abstract: We consider a nine-parameter familiy of 3D quadratic systems, x ˙ = x + P 2 ( x , y , z ) , y ˙ = − y + Q 2 ( x , y , z ) , z ˙ = − z + R 2 ( x , y , z ) , where P 2 , Q 2 , R 2 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.

Keywords: ordinary differential equations; three-dimensional systems; integrability problem; persistent systems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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