Analytical integrability problem for perturbations of cubic Kolmogorov systems

Antonio Algaba, Cristóbal García and Manuel Reyes

Chaos, Solitons & Fractals, 2018, vol. 113, issue C, 1-10

Abstract: We solve, by using normal forms, the analytical integrability problem for differential systems in the plane whose first homogeneous component is a cubic Kolmogorov system whose origin is an isolated singularity. As an application, we give the analytically integrable systems of a class of systems x˙=x(P2+P3),y˙=y(Q2+Q3), with Pi, Qi homogeneous polynomials of degree i. We also prove that for any n ≥ 3, there are analytically integrable perturbations of x˙=xPn,y˙=yQn which are not orbital equivalent to its first homogeneous component.

Keywords: Kolmogorov systems; Integrability; Linearization; Inverse Integrating Factors (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:113:y:2018:i:c:p:1-10

DOI: 10.1016/j.chaos.2018.05.011

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