On the Integrability of Persistent Quadratic Three-Dimensional Systems

Autor:	Brigita Ferčec, Maja Žulj, Matej Mencinger
Jazyk:	angličtina
Rok vydání:	2024
Předmět:	ordinary differential equations three-dimensional systems integrability problem persistent systems Mathematics QA1-939
Zdroj:	Mathematics, Vol 12, Iss 9, p 1338 (2024)
Druh dokumentu:	article
ISSN:	2227-7390
DOI:	10.3390/math12091338
Popis:	We 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.
Databáze:	Directory of Open Access Journals
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