Integrability of Lotka-Volterra type systems of degree 4

Changjian Liu; Guoting Chen; Guanrong Chen

doi:10.1016/j.jmaa.2011.10.056

Integrability of Lotka-Volterra type systems of degree 4

Changjian Liu, Guoting Chen, Guanrong Chen

Department of Electrical Engineering

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

20 Citations (Scopus)

Abstract

We study the integrability of the Lotka-Volterra type systems with 1. :. - (3. q- 1) resonances. We prove some sufficient conditions for the integrabilities of the systems and give some necessary conditions by studying the first two saddle values of the system. In the particular cases of 1. :. - 2, 1. :. - 5 and 1. :. - 8 resonances, we derive necessary and sufficient conditions for the integrabilities of the systems. © 2011 Elsevier Inc.

Original language	English
Pages (from-to)	1107-1116
Journal	Journal of Mathematical Analysis and Applications
Volume	388
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2011.10.056
Publication status	Published - 15 Apr 2012

Research Keywords

Center problem
Integrability
Lotka-Volterra type system
Saddle value

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T1 - Integrability of Lotka-Volterra type systems of degree 4

AU - Liu, Changjian

AU - Chen, Guoting

AU - Chen, Guanrong

PY - 2012/4/15

Y1 - 2012/4/15

N2 - We study the integrability of the Lotka-Volterra type systems with 1. :. - (3. q- 1) resonances. We prove some sufficient conditions for the integrabilities of the systems and give some necessary conditions by studying the first two saddle values of the system. In the particular cases of 1. :. - 2, 1. :. - 5 and 1. :. - 8 resonances, we derive necessary and sufficient conditions for the integrabilities of the systems. © 2011 Elsevier Inc.

AB - We study the integrability of the Lotka-Volterra type systems with 1. :. - (3. q- 1) resonances. We prove some sufficient conditions for the integrabilities of the systems and give some necessary conditions by studying the first two saddle values of the system. In the particular cases of 1. :. - 2, 1. :. - 5 and 1. :. - 8 resonances, we derive necessary and sufficient conditions for the integrabilities of the systems. © 2011 Elsevier Inc.

KW - Center problem

KW - Integrability

KW - Lotka-Volterra type system

KW - Saddle value

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DO - 10.1016/j.jmaa.2011.10.056

M3 - RGC 21 - Publication in refereed journal

SN - 0022-247X

VL - 388

SP - 1107

EP - 1116

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

Integrability of Lotka-Volterra type systems of degree 4

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Research Keywords

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