2021; Physical and Mathematical Sciences, 55(1 (254): 1–11
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EXPLICIT FORM FOR THE FIRST INTEGRAL AND LIMIT CYCLES OF A CLASS OF PLANAR KOLMOGOROV SYSTEMS

Rachid Boukecha*

Received: 2025-01-27 · Published: 2021-05-21

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CC BY-NC 4.0 This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
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Original title
EXPLICIT FORM FOR THE FIRST INTEGRAL AND LIMIT CYCLES OF A CLASS OF PLANAR KOLMOGOROV SYSTEMS
Author
Rachid Boukecha
Published
2021-05-21
Licence
Creative Commons Attribution-NonCommercial 4.0 International
Original
https://doi.org/10.46991/PYSU:A/2021.55.1.01

Abstract

In this paper we characterize the integrability and the non-existence of limit cycles of Kolmogorov systems of the form {x′=x(R(x,y)exp⁡(A(x,y)B(x,y))+P(x,y)exp⁡(C(x,y)D(x,y))),y′=y(R(x,y)exp⁡(A(x,y)B(x,y))+Q(x,y)exp⁡(V(x,y)W(x,y))), where A(x,y), B(x,y), C(x,y), D(x,y), P(x,y), Q(x,y), R(x,y), V(x,y), W(x,y) are homogeneous polynomials of degree a, a, b, b, n, n, m, c, c, respectively. Concrete example exhibiting the applicability of our result is introduced.
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