Dynamics of a family of Lotka-Volterra systems in R3

被引：6

作者：

Llibre, Jaume ^{[1
]}

Martinez, Y. Paulina ^{[2
,3
]}

机构：

[1] Univ Autonoma Barcelona, Fac Ciencies, Dept Matemat, Barcelona 08193, Catalonia, Spain

[2] Ctr Recerca Matemat, Barcelona 08193, Catalonia, Spain

[3] Univ Bio Bio, Fac Ciencias, Dept Matemat, Concepcion, Chile

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2020年 / 199卷

基金：

欧盟地平线“2020”;

关键词：

Lotka-Volterra; Integrability; Phase portraits; Poincare disc; DIFFERENTIAL-EQUATIONS; CLASSIFICATION;

D O I：

10.1016/j.na.2020.111915

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We provide the phase portraits of the 3-dimensional Lotka-Volterra systems (x) over dot = x(y + az), (y) over dot = y(x + z), (z) over dot = bz(- ax + y), for all the values of the parameters a and b, in the finite region and in the infinity region through the Poincare compactification. We also study the integrability of the system. (c) 2020 Elsevier Ltd. All rights reserved.

引用

页数：15

共 50 条

[21] Whence Lotka-Volterra?Conservation laws and integrable systems in ecology
James P. O’Dwyer
[J]. Theoretical Ecology, 2018, 11 : 441 - 452
[22] Classification and Dynamics of Stably Dissipative Three-Dimensional Lotka-Volterra Systems
Liu Haiying
[J]. HIGH PERFORMANCE NETWORKING, COMPUTING, AND COMMUNICATION SYSTEMS, 2011, 163 : 147 - 163
[23] Three-Dimensional Lotka-Volterra Systems with 3:-1:2-Resonance
Aziz, Waleed
Christopher, Colin
Llibre, Jaume
Pantazi, Chara
[J]. MEDITERRANEAN JOURNAL OF MATHEMATICS, 2021, 18 (04)
[24] On the dynamics of Lotka-Volterra equations having an invariant hyperplane
Plank, M
[J]. SIAM JOURNAL ON APPLIED MATHEMATICS, 1999, 59 (05) : 1540 - 1551
[25] Global attractor in retarded competitive Lotka-Volterra systems
Hou, ZY
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2001, 47 (06) : 4037 - 4048
[26] Asymptotic behaviour and bifurcation in competitive Lotka-Volterra Systems
Hou, Zhanyuan
[J]. APPLIED MATHEMATICS LETTERS, 2012, 25 (02) : 195 - 199
[27] Global attractor in autonomous competitive Lotka-Volterra systems
Hou, ZY
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1999, 127 (12) : 3633 - 3642
[28] Permanence and extinction in competitive Lotka-Volterra systems with delays
Hou, Zhanyuan
[J]. NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2011, 12 (04) : 2130 - 2141
[29] Vanishing components in autonomous competitive Lotka-Volterra systems
Hou, Zhanyuan
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2009, 359 (01) : 302 - 310
[30] Integrability of Lotka-Volterra Planar Complex Cubic Systems
Dukaric, Masa
Gine, Jaume
[J]. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2016, 26 (01):

← 1 2 3 4 5 →