On the dynamics of a class of Kolmogorov systems

Llibre, Jaume; Salhi, Tayeb

doi:10.1016/j.amc.2013.09.017

Cited by 15 publications

(14 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the qualitative theory of planar dynamical systems see [5,8,9,10,16,17], one of the most important topics is related to the second part of the unsolved Hilbert 16th problem. There is a huge literature about limit cycles, most of them deal essentially with their detection, their number and their stability and rare are papers concerned by giving them explicitly see [1,2,3,4,12].…”

Section: Introductionmentioning

confidence: 99%

On the dynamics of a class of rational Kolmogorov systems

Boukoucha

Bendjeddou

2021

JNMP

View full text Add to dashboard Cite

Section: Introductionmentioning

confidence: 99%

On the dynamics of a class of rational Kolmogorov systems

Boukoucha

Bendjeddou

2021

JNMP

View full text Add to dashboard Cite

“…Concerning the Kolmogorov systems, most of the studies were limited to study the existence of limit cycles for classes of these systems see [17,20,21,[25][26][27]. To our knowledge, the exact analytic expressions of the limit cycles for a given Kolmogorov system is still unknown except in algebraic case.…”

Section: Introductionmentioning

confidence: 99%

A Class of Quintic Kolmogorov Systems with Explicit Non-algebraic Limit Cycle

Bendjeddou¹,

Grazem

Бенджедду³

et al. 2019

Journal of Siberian Federal University. Mathematics &Amp; Physics

View full text Add to dashboard Cite

Various physical, ecological, economic, etc phenomena are governed by planar differential systems. Sub- sequently, several research studies are interested in the study of limit cycles because of their interest in the understanding of these systems. The aim of this paper is to investigate a class of quintic Kolmogorov systems, namely systems of the form x=xP4 (x;y); y= y Q4 (x; y) ; where P4 and Q4 are quartic polynomials. Within this class, our attention is restricted to study the limit cycle in the realistic quadrant {(x; y) 2 R2; x > 0; y > 0}. According to the hypothesises, the existence of algebraic or non-algebraic limit cycle is proved. Furthermore, this limit cycle is explicitly given in polar coordinates. Some examples are presented in order to illustrate the applicability of our result

show abstract

“…In [2] it is showed the existence of a separatrix dividing the phase plane. In [5] it was characterized non-existence of periodic orbits for the 2-dimensional Kolmogorov systems. A Dulac function for the Kolmogorov system was found [4].…”

Section: Introductionmentioning

confidence: 99%

Stability in a Holling-Tanner predator-prey model like a Kolmogorov system without periodic orbits via Dulac functions

Marín¹,

Ortiz-Ortiz²,

Gutiérrez³

2018

ces

View full text Add to dashboard Cite

In this work, we find Dulac functions for Kolmogorov systems which can be applied to biological models in population. With a well choose of the Dulac function h we obtain stability and a phase diagram without periodic orbits. We prove that there are not periodic orbits at the interior of the first quadrant on the plane. We also obtain a generalized Kolmogorov system and apply this to the Holling-Tanner model and we use time series to understand its behaviour.

show abstract

On the dynamics of a class of Kolmogorov systems

Cited by 15 publications

References 21 publications

On the dynamics of a class of rational Kolmogorov systems

On the dynamics of a class of rational Kolmogorov systems

A Class of Quintic Kolmogorov Systems with Explicit Non-algebraic Limit Cycle

Stability in a Holling-Tanner predator-prey model like a Kolmogorov system without periodic orbits via Dulac functions

Contact Info

Product

Resources

About