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Existence and uniqueness of limit cycles on a cubic kolmogorov differential system in the Predator-Prey relation

Existence and uniqueness of limit cycles on a cubic kolmogorov differential system in the... In this paper, we analyse qualitatively a cubic Kolmogorov system: $$\left\{ \begin{gathered} \frac{{dx}}{{dt}} = x[a_0 + a_1 x - a_3 x^2 - a_4 y + a_5 xy], \hfill \\ \frac{{dy}}{{dt}} = y(x - 1)(1 + by), \hfill \\ \end{gathered} \right.$$ which is one of the mathematical models in ecology describing the interaction between Predator-Prey of two populations; and give the conditions of nonexistence, existence and uniqueness of limit cycles for three different cases. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Existence and uniqueness of limit cycles on a cubic kolmogorov differential system in the Predator-Prey relation

Acta Mathematicae Applicatae Sinica , Volume 4 (3) – Jul 13, 2005

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References (3)

Publisher
Springer Journals
Copyright
Copyright © 1988 by Science Press, Beijing, China and Allerton Press, Inc., New York, U.S.A.
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/BF02006221
Publisher site
See Article on Publisher Site

Abstract

In this paper, we analyse qualitatively a cubic Kolmogorov system: $$\left\{ \begin{gathered} \frac{{dx}}{{dt}} = x[a_0 + a_1 x - a_3 x^2 - a_4 y + a_5 xy], \hfill \\ \frac{{dy}}{{dt}} = y(x - 1)(1 + by), \hfill \\ \end{gathered} \right.$$ which is one of the mathematical models in ecology describing the interaction between Predator-Prey of two populations; and give the conditions of nonexistence, existence and uniqueness of limit cycles for three different cases.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jul 13, 2005

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