1. bookVolume 2021 (2021): Issue 1 (January 2021)
Journal Details
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Format
Journal
eISSN
2544-9990
First Published
30 May 2018
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1 time per year
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English
access type Open Access

On the non existence of periodic orbits for a class of two dimensional Kolmogorov systems

Published Online: 23 Nov 2021
Volume & Issue: Volume 2021 (2021) - Issue 1 (January 2021)
Page range: 1 - 11
Received: 14 Jan 2021
Accepted: 31 Aug 2021
Journal Details
License
Format
Journal
eISSN
2544-9990
First Published
30 May 2018
Publication timeframe
1 time per year
Languages
English
Abstract

In this paper we characterize the integrability and the non-existence of limit cycles of Kolmogorov systems of the form x=x(B1(x,y)ln|A3(x,y)A4(x,y)|+B3(x,y)ln|A1(x,y)A2(x,y)|),y=y(B2(x,y)ln|A5(x,y)A6(x,y)|+B3(x,y)ln|A1(x,y)A2(x,y)|) \matrix{{x' = x\left( {{B_1}\left( {x,y} \right)\ln \left| {{{{A_3}\left( {x,y} \right)} \over {{A_4}\left( {x,y} \right)}}} \right| + {B_3}\left( {x,y} \right)\ln \left| {{{{A_1}\left( {x,y} \right)} \over {{A_2}\left( {x,y} \right)}}} \right|} \right),} \hfill \cr {y' = y\left( {{B_2}\left( {x,y} \right)\ln \left| {{{{A_5}\left( {x,y} \right)} \over {{A_6}\left( {x,y} \right)}}} \right| + {B_3}\left( {x,y} \right)\ln \left| {{{{A_1}\left( {x,y} \right)} \over {{A_2}\left( {x,y} \right)}}} \right|} \right)} \hfill \cr } where A1 (x, y), A2 (x, y), A3 (x, y), A4 (x, y), A5 (x, y), A6 (x, y), B1 (x, y), B2 (x, y), B3 (x, y) are homogeneous polynomials of degree a, a, b, b, c, c, n, n, m respectively. Concrete example exhibiting the applicability of our result is introduced.

Keywords

MSC 2010

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