Conservation laws and symmetries in competitive systems

Lisa Uechi, Tatsuya Akutsu

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

We investigate a conservation law of a system of symmetric 2n-dimensional nonlinear differential equations. We use Lagrangian approach and Noether's theorem to analyze Lotka-Volterra type of competitive system. We observe that the coefficients of the 2n-dimensional nonlinear differential equations are strictly restricted when the system has a conserved quantity, and the relation between a conserved system and Lyapunov function is shown in terms of Noether's theorem. We find that a system of the 2n-dimensional first-order nonlinear differential equations in a symmetric form should appear in a binary-coupled form (BCF), and a BCF has a conserved quantity if parameters satisfy certain conditions. The conservation law manifests characteristic properties of a system of nonlinear differential equations and can be employed to check the accuracy of numerical solutions in the BCF.

Original languageEnglish
Pages (from-to)210-222
Number of pages13
JournalProgress of Theoretical Physics Supplement
Issue number194
Publication statusPublished - 2012
Externally publishedYes

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conservation laws
differential equations
symmetry
theorems
Liapunov functions
coefficients

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)

Cite this

Conservation laws and symmetries in competitive systems. / Uechi, Lisa; Akutsu, Tatsuya.

In: Progress of Theoretical Physics Supplement, No. 194, 2012, p. 210-222.

Research output: Contribution to journalArticle

Uechi, Lisa ; Akutsu, Tatsuya. / Conservation laws and symmetries in competitive systems. In: Progress of Theoretical Physics Supplement. 2012 ; No. 194. pp. 210-222.
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