Limit cycles for two families of cubic systems

被引：5

作者：

Alvarez, M. J. ^{[1
]}

Gasull, A. ^{[2
]}

Prohens, R. ^{[1
]}

机构：

[1] Univ Illes Balears, Dept Matemat & Informat, Palma de Mallorca 07122, Illes Balears, Spain

[2] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Spain

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2012年 / 75卷 / 18期

关键词：

Cubic system; Kolmogorov system; Limit cycle; Bifurcation; PREDATOR-PREY SYSTEMS; STAR-FORMATION; GLOBAL STABILITY; SPIRAL GALAXIES; MODEL;

D O I：

10.1016/j.na.2012.07.012

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study the number of limit cycles of two families of cubic systems introduced in previous papers to model real phenomena. The first one is motivated by a model of star formation histories in giant spiral galaxies and the second one comes from a model of Volterra type. To prove our results we develop a new criterion on the nonexistence of periodic orbits and we extend a well-known criterion on the uniqueness of limit cycles due to Kuang and Freedman. Both results allow to reduce the problem to the control of the sign of certain functions that are treated by algebraic tools. Moreover, in both cases, we prove that when the limit cycles exist they are non-algebraic. (C) 2012 Elsevier Ltd. All rights reserved.

引用

页码：6402 / 6417

页数：16

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